Ok, I hate to rain on your parade, and at the risk of offending the Oregonians here, I have some reservations about this grand plan.
If this is really going to be your first real backpacking trip, going alone isn't the greatest idea. However, I've traveled alone and depending on where you are, it can be a lot of fun because you tend to meet people along the way you might not otherwise meet (and that includes, in your case, girls). On the other hand, you could disappear and no one would have a clue what happened to you-been there, done that-not the disappearing part, but the hiking alone where absolutely no one knew where I was part.
But, aside from that, let's assume you do some shorter trips in FL, learn to use your gear and are ready to go. If I was you, I would head to Yosemite and here's why:
1. You don't need a car-you can fly into San Francisco and take a bus to the park;
2. The scenery can't be beat and it is wildly varied;
3. The park offers every type of accommodation and has its own internal bus system;
4. You can hike into the backcountry on dozens of different trails and even hike part of the John Muir Trail if you like; there are guidebooks that you can use for trip planning-Rough Guides makes a really nice one;
5. The park has plenty of infrastructure, including gear and rental shops for bear canisters (a must in the high country), supermarkets, fast food places;
6. If you are alone, I would take along a SPOT (it's a gadget that you use to notify friends if you get hurt or lost) or a PLB (a different gadget that notifies SAR to come look for you); Yosemite has a very sophisticated SAR team that looks for people all the time.
Don't get me started, you know how I get.