Arriving by plane in Cancun, you can get on a bus straight from the airport to Playa del Carmen. That will save you an hour compared to taking the bus to downtown Cancun and changing.
In Playa del Carmen you can find another bus leaving for Tulum, probably within the hour. Do so. There's nothing worth seeing or doing in Playa del Carmen.
Arriving in Tulum you can find accommodation close to the bus station (ADO), or you can invest 30 pesos in getting a taxi to take you to the beach strip, which really is lovely, so consider that.
Get up really early and be at the gate before they open at 8 in the morning. It's half an hours walk from downtown Tulum, and can be considerably longer from the beach hotels. GPS coordinates are N20.12.910 W87.25.831. Spend your first hour wisely, because after that there will be tourism mayhem going on all around you.
If you're not that into Mayan ruins, you may be back at your hotel before check-out time, making it possible to continue your journey the same day. I think, however, that a better way to spend your day is on the beach. The one inside the Tulum archeological zone is beautiful, but a bit too crowded. Try some of the beaches further south for more peace.
Get an early morning bus (ADO) to Chetumal. It's a 3-4 hour drive. In Chetumal you'll arrive at the "wrong" bus station. Get a taxi (20 pesos) to the "Nuevo Mercado Lazaro Cardenas", where there are inexpensive buses to Belize leaving almost every hour. Get one that goes to Belize City without changing buses.
You will arrive in Belize City before dark, but too late to catch a boat to one of the islands nearby. Get a taxi to take you to where you will stay for the night. The Fort George area is really safe and with several good restaurants. A taxi there should cost 3-4 US dollars.
It's easy to while away a day on the mainland before you head for the islands. Start by going back to the bus station. Walking is fine, during the day the city centre is a perfectly safe place to be. Get on any bus bound for San Ignacio and/or Belmopan. Tell them you're going to Belize Zoo, and they will drop you off there, it's right next to the highway 45-55 minutes from Belize City.
Belize Zoo is a great place to sit down with the animals and get to know them. They're all fairly tame and curious about people. If you ask nicely and pay 50 US dollars, they'll even let you get inside the jaguar closure and interact a bit with Junior.
To get back to Belize City, just walk back to the main road and wait. There's a bus stop just outside the zoo entrance, but not every bus will stop there. Just try waving them all down, eventually you will get on a bus, although it may take an hour for this to happen. The best other option is to rent a car for the day, but that will cost a lot more.
Back in Belize, just walk around and explore. Strange sights are everywhere. For the sunset, get to the lighthouse at the end of Fort George and enjoy.
There are several boats leaving for Caye Caulker and Ambergris Caye every day. Caulker is smaller and caters more for the backpacker crowd, while Ambergris is more developed and has more options in all levels of comfort. They're both good islands to visit and you can do roughly the same daytrips from both of them, but if you want to just stay on the island and explore, Ambergris has more to offer.
Obvious activities are sunbathing, snorkelling, diving, windsurfing, beachcombing, eating, drinking and sailing. On Ambergris you can do a bit of hiking as well.
It's possible to go by plane from Ambergris Caye to Flores in Guatemala, but it costs quite a lot more than doing the boat+bus thing. First there's a flight from Ambergris to Belize City, then there's a wait, and then there's another flight from Belize City to Guatemala. All in all, I think going by road is a more interesting day, but flying is of course quicker.
If you get the first boat in the morning from the Cayes, you'll arrive in Belize City just in time for getting the bus to Flores that leaves from outside the boat terminal. You have time to pay when you arrive in Belize City, so you don't have to book it from the islands, although that may be a good idea in case the bus gets full.
You can choose between going to Flores or straight to Tikal. If you choose Tikal, and you should, the comfortable bus from Belize City will stop somewhere before Flores and transfer you to a less comfortable bus heading for Tikal. You'll arrive in Tikal late in the afternoon. There are two hotels where you can stay just next to the Tikal complex. They're quite expensive, but worth it for the location. If you buy your tickets after 3 in the afternoon, you can use them both that day and the next, and you can go inside the park the next morning possibly even before the ticket office opens. For cheaper accommodation, get off the bus at El Remate. It's quite nice there, and you can arrange early morning transport with or without guide to Tikal for the next morning from there as well.
Spend the morning exploring the complex carefully. There is a lot to see, so bring lots of water and good shoes. When you're done, go to the tourist information booth and they'll sell you a ticket for minibus transportation to Flores, probably at a lower price than you can get by dealing directly with the drivers.
In Flores you will have no problem finding somewhere to stay and something to eat. Go for a walk through as many of its streets as possible. It's a beautiful place. Also, have any of the tourism booths book your trip to Chetumal for the next day, or go down to the office near the INGUAT tourism information at the entrance to the island to deal directly with the bus company.
This day will be spent on a bus. They pick you up at your hotel, included in the price.
When you arrive at the Mexican border, there will probably be a fairly long wait. During that time touts will come up to you and offer direct buses to several destinations, leaving from the border. Those buses are legit, but you may have to wait a long time for them to fill up, and they may travel a route that includes a lot of stops, making them a slow option. It's probably better to stick with the bus you're on all the way to the bus station in Chetumal. (It's just 15 minutes or so from the border.)
By now it's probably so late in the day and you're so tired that you may want to stay the night in Chetumal. There are several really nice places to stay, and they are much cheaper than what you'll pay for similar rooms further north along the Mexican coast, so go for it. There's not much to see or do in Chetumal, but the new Biouniverzoo thing really impressed me. You have time to check it out the next day and still be able to reach Chichen Itza by bus before dark.
You probably won't find a direct bus to Chichen Itza, so the quickest option is to take a bus to Tulum (of which there are many) and then continue on to Chichen Itza. You can also take a direct bus to Merida and then continue to Chichen Itza, but that's a longer distance to cover. What is best depends on when you arrive at the bus station.
To see Chichen Itza you can either stay in Pisté, where there are many cheap places to stay, or you can stay right at the Chichen Itza complex at a much higher price. Check the Internet for special deals there, but expect to pay around 100 US dollars for a double room in the best case. In addition, you'll have to take a taxi from where the bus drops you off and to the expensive places in the Mayaland park just on the other side of Chichen Itza. Worst case, a lot more. Wherever you stay, consider going to see the nightly sound and light "show". It's not terribly interesting, but you get to see a few details you can't see during the day. Also, there's probably not much else going on in the evening there...
Again, get up really early and rush in the gate as soon as it opens. You'll probably get in a little bit earlier if you stay at the Mayaland complex. Treasure your time wandering in peace and quiet among the temples and ruins before the crowds arrive. When it gets too busy you might as well leave the park to avoid going crazy.
Get to the bus station in Pisté and there will soon be a bus to take you to Cancun. It takes roughly three hours.
In Cancun you can either stay near the bus station (cheap, just a bus ride away from the beach and the airport), on the beach strip of hotels (Zona Hotelera, expensive, but right on the beach) or at an airport hotel (not cheap, not real expensive, and with free transfers both to the beach and the airport). Keep in mind that in the hotel zone all prices are much, much higher than anywhere else, both for taxis, meals and activities.
See? That wasn't too difficult, was it? And we crammed a lot of contents into those two weeks, with a day to spare.
If you have any further questions, feel free to ask in an e-mail.