Sorry to hear about the reason for your getting the fishing rod, but welcome to the fly fishing fraternity.
Used to live in California (Bay Area) and have fished down your way before as well (Pismo Beach area) so might be able to offer you some more specific advice, though what has been provided thus far has been great.
To answer your initial question, almost any fish will take a "fly", provided that the "fly" resemlbes something they are interested in eating. Lets think about what you have available to you.
Trout: I have heard of some trout in the streams near SLO, but think you would do better for trout heading up to the Sierras (check out California Blue Ribbon Trout Streams, by Bill Sunderland)
Bluegills and Bass: Pretty much any stillwater in your area will have some. With some polarized glasses you may be able to see them, and the advice on lily pads and weed beds is good. Small poppers in the early AM or evening might be your best bet....in the heat of an SLO summer fish may head deep.
White bass: lake nacimiento just north of you (thought this is a boat affair)
Stripers: abit further north to San Luis Reservoir and the forebay...tube works well.
Salt water: right off the beach at Pismo or Avila Beach you will find Surf Perch, croakers, halibut, all very willing to take a fly. This is generally the area for a sinking line, which is perhaps best left until you have a good grasp of the techniques of casting.
Casting: I learned from reading a book, but would recommend that you look at a lesson or two either from someone who is a proficient caster, or preferrable from an instructor (I know there is a fly shop in SLO, although the name escapes me)
Doesn't have to be far, but being able to lay out 30-40 feet of line in the general vicinity of where you would like, will get you into the bluegills and bass.
Have loads of fun.