It's nice descent hotel, fairly far from the Old City - not that it's the only enterntainment out there, but more of a tourist must see places like Eiffel tower in Paris.
1) While staying in JW Mariott try Sunday brunch.
2) At the south side of the building there is a Buddha Bar - nice lounge place to chill.
3) Use apps like Uber or Taxity for taxis - dirt cheap, have CC payment option so you don't have to carry a change or talk to a driver at all. If you don't have airport transfer included or prepaid by company then tell the receptionist to pre-order you an airport transfer service from 189 taxi service and mention Business tier. Roughly 10-15 CAD including tips.
4) Half/km down west there is a Port Baku aka Fashion Ave. - lots of places to eat, shop or just talk to the people.

Have fun there.