It's possible to rent a car if you're under 25, just not necessarily from the rental companies that spend millions on advertising annually. Can't help much more than that. You might try Rent-A-Wreck.
The city of Irwindale itself is interesting because the population is 1500 in 9 square miles. That tells you it's mostly home to industry and offices, the notable exception being the Irwindale Speedway, which as you may figure, hosts racing and drifting competitions. I'm not in the loop on these things so I can't tell you what's coming up. Anyway there are tons of people in the cities next door like Baldwin Park, but I don't usually go out there so I can't recommend much else. Pasadena is fairly close and has a pretty nice downtown area. There's a Fry's, the world's best physical electronics store, fairly close by in City of Industry if you want to geek out.
If you want to do something outdoors, you're in luck because the Angeles National Forest is just a few miles north. Well, I've never gone camping there, but people do. However I have gone hiking there. The mountains go up to about 10,000 ft elevation (few that high; 5,000 is probably the average). You can drive around them or hike your way to the top of them if you're in good shape. Someone else probably knows about camping, and there's a thread about it on the SoCal board if you're interested.
Getting a little farther away, sure, Santa Monica will work, it's a nice place. If you want to go swimming, it maybe doesn't have THE cleanest water, but eh it's the summer, probably not an issue. You know, I do hear the Orange County beaches like Newport and Huntington mentioned are among the best, but I've never been to them. (I'm not big on the beach thing. Once I had a dream I was trying to surf, that's about it.) Some other nice LA County beaches are Manhattan and Hermosa, which are some miles south of Santa Monica but not TOO far. If you drive to Santa Monica, do it midday if you can, and if not, prefer the afternoon over the morning. If you drive from Irwindale to Santa Monica during the hours of about 7 AM to 10 AM (on a weekday) you will probably sit in a lot more heinous traffic than you want to sit in. You can also find not-so-urban beaches further north in Ventura and Santa Barbara counties. Depends how far you want/are willing to drive.
To plug West Hollywood, there are lots of bars, clubs, restaurants, etc here, especially on the Sunset Strip. (Also a lot on Santa Monica Blvd., but the bars there tend to be of the homosexual persuasion.) The standard tourist stuff like the Walk of Fame and Chinese Theater are further east in Hollywood proper. There are also a lot of bars and clubs there in Hollywood too that are celeb-frequented. I don't really have specific recommendations for bars because I'm still (still) under 21. For live music (rock) though, I can say the Roxy Theater and Key Club are pretty good, also the House of Blues and Viper Room are noted.
To find out what to do, pick up a copy of the free LA Weekly published every Thursday, or go to
http://www.laweekly.com. If you want to hang out some time, that'd be cool, but I'm no tour guide, so you should probably have something that you want to do in mind first.
Also, I may go to Six Flags Magic Mountain (which is where to go if you like rollercoasters, but on second thought perhaps that's not your thing) some time in the next month, and I'm definitely going to Ozzfest on August 20th (that's going to be east of Irwindale near San Bernardino) in case you're also into that.