Trust TripAdvisor reviews for the B&B decision, they are always spot on in my experiences with everything about travel. Pick a place in Capitol Hill neighborhood or across the I-25 walking bridge in Highlands, both hoods are old mixed with new with an easy walk to downtown. Even better, you can rent a bike, to get info look on denver.bcycle.com which is a fantastic way to get around town. Our weather is usually incredible, you will probably want to be outside for your discoveries.
A short trip that is close in the mountains is up Mt Evans via Evergreen then down to Idaho Springs, can make stop at Red Rocks on the way up or back, plenty of hiking trails and a river along this path. Could be a 1/2 day trip so you can experience the wonderous mountains so close to Denver.
If you like sports take in a Rockies baseball game, at one of the best sports venues in North America. Have fun!