The Hyatt is right there where the bats come out, just on the south side of the river. Four Seasons is on the north side of the river, just a couple of blocks away from the Congress St. Bridge. The Raddison is right there at Congress & Caesar Chavez (formerly 1st St.) but it is more of an average place, not a 3-4 star.
The Children's Museum is an easy walk from The Raddison or Four Seasons. They're building a "W" hotel right down in the district, but I don't think it is ready yet- it will be one of those 4-5 star expeiences.

Thanks for all of the wonderful suggestions!

One more question (thanks for bearing with me!). I heard something about a train near Barton Springs for kids? Is this correct or am I confused?

There is a small train in Zilker park (same place as Barton Springs), as well as a large playground and canoes for rent. It takes about a 10min loop in the park. Can be a fun ride for 3-4-5 yr olds

http://www.ci.austin.tx.us/parks/zilker.htm

There's also a concession stand right there that sells ice cream. (Hands clasped) "Pleeeeease. Pleeeease!!"

Even if you decide NOT to go into Barton Springs you can enjoy the cool water. Just below the pool where the creek flows out of the pool you can wade & splash in the cool water for free. Water is cold and flowing, and rocks are slippery so a kid may need hand held. It's not my favorite place, but if you go to the train be prepared for daughter to want to go in the water, even if it's just wading across the creek. I advise you to pack water shoes and a towel just in case.

The reason it's not my favorite place is there are often a lot of dogs in the area on land, plus what they leave behind & owners don't pick up.

Embassy Suites- on the corner of Congress & Barton Springs Drive.
If you want to see the bats, you need to wait til later in the spring. There is a bat sculpture right on the corner by the hotel, but this time of year, that is the only kind of bat you'll see.

You might also check out the Downtown Omni- it is on Eight St. between Brazos & San Jacinto. Walking distance (with little one in stroller) to Chidlren's Museum.
Probably closest to the Museum is the Radisson. The new "W" hotel has opened, but they're really expensive! You might also check out and see if any specials at the Four Seasons- they're right on the lake (as is the Radisson) and next door to Shoreline Grill.

It's really nice of you to respond but since the OP was going to Austin a year and a half ago, this might be too late.

Kathi_Thomas, welcome back to the forums! It's nice to see people coming back who have been absent for a while. Please check out the new threads and add your travel expertise and recent experiences to them! Saige