The Marriot (In Panjim/Marimar?) has a small selection of shops about 5/10 minutes walk away. To get to the center of Panjim it's probably more like 20/25 mins walk (At a guess), it's a posh hotel (never got past reception myself ), but can feel a little 'out on it's own' as it's a good 20 minute taxi drive to Calangute/Candolim area and the 'buzz'...

I would get a taxi to take you. You can either order one from the hotel or pick one up just outside (a lot cheaper this way). Wouldn't walk into Panjim as very hot. You could always jump the bus (which we did a couple of times) or get toot toot (!).