Well you can, but it's about 4kms away, so you are better off getting a local bemo or taxi.What ever you do, do not be tempted to get a pony cart to bring you back to the hotel. The carts have no brakes and I've heard of some terrible accidents.
If you are brave you can also rent a motorbike which is very handy for tootling into Senggigi for fresh supplies of mixers, snacks etc. The roads are reasonably quiet, but a couple of hills to negotiate and the view is stunning so easy to get distracted.
Lombok is not the shoppers paradise that Bali is. I usually advise people to get a few special souvenirs in Lombok, particularly from places they visit, and leave the major shopping for Bali.
Glad you made a choice on accom - I'm sure you will love it there.