The Yucatan Penninsula is easy biking. There are few hills and lots of small roads that bike tourists will love. We stayed away from the tourist-ridden east coast (Cancun) so the comments here apply to the interior and northern coast (see map for the route). We visited the Yucatan in late December and early January. The weather at this time was excellent: no rain and ideal temperatures. Food is fairly easy to come by and generally very good. Fresh tortillas abound. Expect a "mill" on the center square of all small towns. Also try tortilla soup - with limes and chicken stock. Give up on the idea of good coffee; you'll be drinking Nescafe.
The ride along the north coast is one of the best on the planet. It's wetlands, full of birds and, though not a nature reserve, it is undeveloped wet lands. It'll be you and the birds (and the occasional crocodile) on the ride. Make sure that you have binoculars and stop frequently to looks at the flocks.
We saw no evidence of crime and felt completely safe everywhere we went.