We stay at the HR Houston Downtown frequently. An early breakfast shouldn't be an issue. Both Einstein's Bagels and Shula's open for breakfast at 6am (during the week; Shula's doesn't open until 8 on weekends). Einstein's offers coffee, drinks, and bagel sandwiches while Shula's has a nice buffet and full breakfast menu available. We much prefer breakfast at Shula's compared to the offering at the HR Houston Galleria. I can't say much about the fitness center, although I understand it does have some Peloton bikes. You're just a few blocks from Buffalo Bayou Park with some nice walking/running paths if that's of interest.