Overnighting at the Maya ruins of Chichen Itza, Yucatan is easy. Plenty of hotels are in Piste, within walking distance of Chichen Itza. Over the 30 years that I have visited Chichen Itza on archaeological research, or led study groups to Chichen Itza, I have stayed in most of the hotels, from the Hacienda Chichen, the Mayaland, the Mision, but in recent years I have always stayed in the Piramide Inn Resort.
Prices are more reasonable at the Piramide Inn hotel, always plenty of parking, and the hotel is family owned in the second generation. The hotel's web site is www.piramideinn.com. One of the main decorations of the hotel was borrowed from the front cover of my book, "Monsters and Men in Maya Art," ADEVA, Graz (Austria) and FLAAR (St Louis), 1987 (still in print from FLAAR).
Piramide Inn, tel (985) 851-0115 (in Mexico). From USA: Fax: 011-52-(985) 851-0114, Tel: 011-52-(985) 851-0115. International: : Fax: 52- (Number) (985) 85-1-01-14, Tel: 52- (Number) (985) 85-1-01-15
In Merida I tended to stay in the central area until prices got out of line with what they offered. Hotel Merida is nice because it is safe (as is everything in Yucatan) but traffic noise is rather rough. I stayed in the Posada Toledo for years but their prices are too high for what you get. I figured if I need to pay I might as well enjoy the stay, so I tried the Hyatt Regency Merida. It is within walking distance of the Palacio Canton, Merida's archaeology museum (presuming the temperature is below boiling point and presuming you can walk a few blocks). Actually I routinely walk from the Hyatt all the way into downtown, though a horse and buggy ride would be easier on a warm Merida day.