I need a room under $300 that is centrally located, well priced with many amenities. Traveling with 13yr old granddaughter. Spring or summer trip? Which would be better? would a 4 or 5 day trip. Also what are the must see and do things with a 13 yr old?
I would recommend the Hyatt Place Austin Downtown (211 E 3rd St) I actually recently stayed there when my place got flooded down the street. It's a great location downtown, big rooms, and a great breakfast. You can pretty much walk anywhere. I'd also recommend Radisson Hotel Austin - Town Lake. It has a new great restaurant inside of it and a great place to watch the bats from at sunset. Even if you don't stay there, I'd recommend the restaurant, Chavez, for happy hour and appetizers just before sunset. I can't speak for the Radisson hotel rooms or service itself just that it's a good location.
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Embassy Suites on S. Congress is near downtown. You can walk it if you're enthusiastic, or they have a free shuttle. Embassy Suites are generally pretty good in price. Unless there's some kind of major event in town, you should be able to get something there for around $150 a night, and will have plenty of room for you and your grand daughter. If possible I would say go in late spring, or early Summer. Early spring, and you're looking at getting rained on. Middle to late summer and you're looking at days that are so hot you might not want to be out.
Try the Hotel San Jose. Cool, hip, boutique hotel located right on South Congress. The W Austin Hotel is located right downtown and the hip large format hotel other than the Four Seasons. We have many hotels under construction as we speak which was much needed. Activities are running/walking around Lady Bird Lake, shopping/eating around the 2nd street district. Uchi is the well known sushi style restaurant that gets all the press. Worth going to but try some of the newer places like Swift's Attic or Hopdoddy Burger Bar.
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It's a little out of the way, but try Austin Marriott South. You'll get a great room for your dollar, and they have a free shuttle that takes you to the middle of downtown (it's about a 5 minute drive). You can enjoy the best of downtown life and then retire to a more quiet area for some rest.
I'm with Michael on using AirBnB, especially with your price point, you can get a very nice place in downtown. Also, definitely go in spring. We get strings of triple digit days in summer.
What's your granddaughter interested in? There's tons to do and it will depend on what she enjoys.