I didn't use the gym, so can't help. The beach is hemmed in by a headland to the north and the river estuary at the other end: you might look a bit hamster-ish running up and down it. The headland is good for clambering over though.

The hotels attracts conventions and weddings from out of state. Goa is very popular withhin India because of its relaxed attitudes to alcohol and other forms of relaxation..... Families also visit over holiday seasons. I mention all this because it may conflict with your hopes of R&R - you could ask the hotel if they have any events booked over the period.

Cheers, Ian