Hamilton Place area is fairly nice and about a 15 minute drive from downtown. There are a number of chain hotels - a new Hilton and I believe an Embassy Suites are being built now - as well as a number of popular chain restaurants and big box stores. You have two choices for driving into downtown - I-75/I-24 and Hwy 53/Amicola Hwy, both of which take about the same amount of time. Parking downtown can be tricky if you are not familiar with the area. Street parking is largely metered and there are a number of monitored private lots and decks.

To me, the choice would probably come down to what you are looking for in terms of spending your downtime around the race. If you want to see Chattanooga, stay downtown. There are a number of good local restaurants, bars, museums, movie theater, and great places to generally walk around and enjoy the scenery. Hamilton Place offers conveniences, but is really no different than similar development sites in most large towns around the country centered around a shopping mall. If you are traveling with kids, I would definitely recommend downtown if for nothing else to avoid having to worry about parking. Most of the hotels are very close to transition and should be near the run course.