First of all, if it's at all possible, fly into John Wayne/Orange County Airport (SNA). You'll save yourself a lot of time and grief. You'd be about 15 minutes from your hotel and they may have a free shuttle which would save about $50.00 per person each way from LAX (best guesstimate).
Regardless of how you get to the hotel, there is an Enterprise Car Rental location within a couple of blocks. Get their weekend special at 50% off. Rent the smallest car they have and you're probably in at about $15.00/day with 100 free miles per day. You wont be going that far but having the car will give you access to a lot of great restaurants, beaches, shopping, etc. that otherwise would be prohibitive if you had to walk or take a cab.
There is a Vespa Scooter store near your hotel but I don't know if they rent or are sales only.
Besides the restaurants mentioned above you might like some of the following: Bluewater Grill and The Cannery on Lido Peninsula. Mama Gina's, 333 Bayside and Bayside, all near the intersection of PCH and Bayside. The Landing, Sienna and Cabo Cantina on the Balboa Peninsula near the Balboa Pier.
For additional info go to:
www.visitnewportbeach.com. There is a spot on there that you can use to request them to send you a visitor guide. It has an excellent map in it that will be very handy in getting around Newport and planning your activities.