Hi, we are in the Torquay area, not too far from Plymouth, so can't really help you with places that the "locals" hang out. However, there are two eating establishments that I would highly recommend 1) Tanner Bros. restaurant, James Tanner is one of the chefs on Ready, Steady Cook, does nice food and its in a beautiful old building, 2) Captain Jasper's, not posh and probably not healthy, but they do a pretty good hamburger! Its down on the Barbican (which is a must see, Mayflower steps are there).
Not sure about beaches in that area, but the Torbay (that would be Torquay & Paignton) are alright and hubby said that Burgh Island and Thurlestone are really nice.
If I can think of anything, will let you know! Have fun!!