I have been on numerous trips in the Sierra range and along the coast, but have yet to go on a "real" backcountry excursion. I'd like to find a place in Northern California where I could pull over and start hiking; no permit and no trails. Any suggestions?
Please define what you mean by "northern California"? Everyone has a different idea of what this is!
There are lots of no-permit (or at least just self-registration) areas. In fact most Forest Service areas are self-registraion off-season. If you want to go in the Sierra without permit hastles, go Oct-May.
Off-trail travel in the coast range is brutal to nearly impossible. Your are kidding yourself if you think this is fun! Nice little-used trails in the Marble Mountains, Snow Mountain wilderness, Trinity Wilderness. Yes, you have to get a permit. No real hassles - go into a FS office and just get one. We all have to bend a little to comply with regulations. This is also a good way to find out about the latest conditions. I find the FS personnel quite helpful.
Warner Wilderness - far northeast corner of California. Another nice area - best done early season - gets really dry and hot later. This is a small wilderness, but has challenging travel. Trails are so little used that you have to be a good tracker to find some. No permits needed.
The peaks east of the Sierra from Bridgeport to Lee Vining area are seldom used. Tioybe National Forest. It is really easy to pick up a permit in their Bridgeport office - few quotas for those areas.
Although it is farther south than you want to go, if you want a real adventure with no trails, no permits in really tough challenging country - go to the east side of the White Mountains. This is also an early-season area. Best to do right now. Once the snow melts, there is little water.
You had better be an experienced off-trail backpacker with good navigation skills to do these. I may be wrong (and pardon me if I am) but it sounds like you want "Survivor Man" experiences and are unwilling to bend politically (get a permit). Honestly, the best off-trail travel is the high Sierra. I go out for 8 days without seeing anyone. Bite the bullet and get a permit and see the best country!
Part of backpacking is learning to work within the permit system. I can relate to your frustration with permits and such on the coast or Bay Area. It seems like this highly populated area does all it can to discourage backpacking with most areas booked weeks in advanced. It is not that bad if you get out of the coastal areas.
There are reserved permits (that cost $ and you have to apply for - a bit intimidating paperwork at first) and there are "first come" permits that are very easy to get. Almost all Forest Service areas have offices near where you will want to go. Walk in, get a permit (you will have to show ID to get the annual fire permit the first time you get a specific trip permit). They give you a short "Leave no Trace" lecture and fire safety lecture. Certain trails have "quotas", others do not. If you choose a no-quota trail, you will always get a permit. If you choose a quota trail first-come permit just be sure to have a few other options so if you do not get your initial request you have the maps you need to do the alternatives. Also, each forest has a web site - and may list the remaining reserved slots. If there is a reserved slot remaining, chances are there will be plenty of "first come" permits available.
For your first backpack, I would NOT recommend an off-trail route. A trail route is better - you certainly can get half mile or more off the trail to set up camp and have solitude. If you are "self teaching" yourself backpacking, you need to start out easy and incrementally increase difficulty while you gain experience. Definitely DO NOT go off-trail until you have good navigational skills (this means read a map - not just follow a GPS).
Also, how far are you willing to drive? An easy overnight starter trip would be the trail up the Mokulmne River from Salt Springs Reservoir. Not many people, no permit hassles (in fact I do this without a permit). It is relatively short (12-miles round trip). There are two roads to Salt Springs Reservoir - the shortest from Hams Station - drop on paved road to the reservoir - and if this is not open due to snow, you can take a long dirt-road up the river.
I have thought for some time now that the Mokelumne above Salt looked good on a map. I'll have to try that sometime. A really nice adventure would be to continue up to the area of 4th of July Lake. Also, another nice area for practicing one's skills, both on and off trail, and which has no quota system ( permits are required, but it is not a problem to get them and they're free) is the Emigrant Wilderness, along Highway 108. But work on those map skills before you do anything off-trail. People get lost every year, not knowing what they're doing.