You can get to Colima by plane only from Mexico City by AeroMar. Airport is located 15km north, outside the city. To get to the downtown your only option is a taxi, which will cost $20.00 USD.
You could also fly to Guadalajara, which is Mexico's second largest city, and where there are more flight options. From there you could take a bus (25 usd), which will take 3 hours to get to Colima bus station and from there to the down town a cab will charge you 2 or 3 US dollars.
Parque de la Piedra Lisa. This park offers a science museum, a playground and several recreational areas, the main attraction is a volcanic stone called la piedra lisa that has the form of a slide and the legend says that once you slide on it you will always come back. The stone comes from the volcano 32 kilometers away from the city, the park was built around this monolithic slide rock. 
Museo de arqueología Pinacoteca de la Universidad Parque regional Catedral de Colima Jardín Libertad Jardín Nuñez
You can also sleep downtown in the Hotel Ceballos (Best Western) or Hotel America.
Just out of the downtown you find the hotel Maria Isabel and at the edge of town is a Fiesta Inn.