Hotel: Another poster found a good deal ($110?) at the downtown Stephen Austin Intercontinental Hotel. If you can get a deal like that, grab it.
Nice dinner: Tough one with a baby (and I've been there!). Problem with most restaurants is the ambient noise, which drove our daughter nuts. A few restaurants still make her uncomfortable. One nice restaurant that passed the noise test was Chez Nous, a French restaurant off Sixth Street. It's very bistro like and smallish. Another nice restaurant, actually more expensive, is the Shoreline Grill, but only if you sit on the outside patio. Inside is way too noisy. Other favorites (i.e. Castle Hill, Manuel's) are too noisy for a kiddo.
Family fun: Zilker Park. Tour the botanical gardens and take your daughter on a ride of the Zilker Zephyr. If you're coming here before the end of April, visit the Ladybird Wildflower Center. I was just there and look forward to go back once again this spring.