The city offers so many different panoramic views. One of my favorites is the way the Alps plunge into the Mediterranean as seen from the northern most tip of the Promenade. Another great view is looking out over the harbor and Old Town from the chateau on the hill. Two very different vistas! As for the water, there are so many shades of blue, you can't begin to comprehend it until you see the sun sparkling off the water and changing colors right before your eyes. The blue sky meets the blue of the water meets the pewter blue pebbles of the beach.
While the rocky beach is a bit shocking at first, I came to really appreciate not leaving with a bag/shoes full of sand every time I went to the beach. It is also beneficial in that the water stays impeccably clear because there isn't a lot of sand being churned up with the waves. Just buy a cheap beach mat from any market or shop and lay a towel down on top of it, or just go to one of the resorts and pay to rent a lounge chair for the day!
Quick Tips:
If it is your first time in Nice, I highly recommend getting a map and just walking all over the place the first day or two. Orient yourself and then plan to spend a bit of time in each section of town.
Best Way To Get Around:
It is easy to fly into Nice using EasyJet or one of the discount airlines from London or Paris. Directly from the US, it's not so cheap. Once you are there, the public transportation is relatively easy, even if you don't speak French (just do your homework about how the fares work). It's a cinch if you just take the bus along the road that follows the Promenade. The bay is a lot longer than a lot of people expect. It is a few miles in length.
A shuttle into the city center leaves the airport regularly and costs about each way. This is probably the cheapest way to get into the heart of it all. Quite frankly, I suggest just walking everywhere, but take bottled water with you! It's hot!