There are multiple ferry stops in Cancun to Isla Mujeres, the closest to your hotel would be a 15 min taxi ride. I The r/t fare is US$15 and it takes about 30 minutes. Once on the island, I imagine you could get a taxi to the beach, but I would suggest making a left out of the terminal and just keep walking along the beach. Theres are some high end resorts with beach side restaurants and beautiful white sand beaches along the way. On the way back to the ferry terminal walk through the town and you can visit the shoppes.
As for getting pesos, there are a couple of ATM's as you exit customs in CUN, but you'll find many places take US $ (I didn't even see a peso price quoted for the ferry).
Last time I was there I stayed at the Hyatt (Top of the 7), and it was a 10 min walk to the ferry, I will be back in CUN in June and will also be staying at the Lagunamar, so I'd be interested in your thoughts on that property. The only restaurant I sampled on my 1 night stay was La Distilleria, which I found fine, but others seem to think it a bit pricey.