I don't think that you mentioned what time of year you plan on visiting. Merida is a lovely city. My husband's family lives there, so we head there several times of year. But I won't go in the summer. It is hot as hades!
In all the times that we've gone - we've always taken the bus. It's easy and it's comfortable. No dealing with crazy city traffic and parking. Since you're thinking about staying downtown - every thing will be in easy walking distance.
On the main square there are at least two tourism offices. Check them out. The staff there are incredibly helpful and will give you a great overview of events. One thing that Merida has in abundance are cultural events. They'll have information about the free walking tour as well as the bus tours (there are two - we've taken both and enjoyed them). They may also be able to point you in the direction of a tour of the various churches. All of which are beautiful.
Also check out the Yucatan Today
One thing that you don't want to miss is the weekend in Merida. Saturday night there will be an open air market and probably folk dancing at the park at the end of the Paseo Montejo. Sunday (Merida en Domingo) the square will be filled with artestians - there will be dancing in streets, restaurants will move their tables outdoors etc. etc.
You definitely want to walk the Paseo de Montejo and check out the beautiful homes (several of which are now museums). And the mercardo is not to be missed. Plan on getting lost - you'll eventually find your way back out!
I also highly recommend taking a tour to Uxmal. Stay for the night show - it is spectacular. Your hotel can set it up. Generally the tour includes transportation to and from, dinner and the night show (you'll pay extra for headphones to listen to the show in a language other than spanish).
If you go Jan/Feb time frame - head to Celestun (again the hotel can set up the tour). You'll see Flamingos, tour mangroves, have lunch on the beach and do some serious shell collecting.
El Colon on the square is a great place to people watch while enjoying a cool and refreshing ice cream. La Chaya Maya is a great little restaurant that serves authentic Yucatecan food http://www.yucatanliving.com/merida-restaurants/la-chaya-maya.htm