Internet in my room was iffy -- I had to keep logging back in on my iPad -- but I didn't have a problem in the breakfast room/restaurant in the basement. I was on the 6th (top) floor, and I think the room was far from the router.
However, there is no gym. However, it is on Bush, and Powell between Sutter (one block south) and Bush is really steep. You won't need a gym walking around San Francisco.