If you're in Fallbrook it's not all that far of a drive over to Anza Borrego. There are some very scenic trails that you can do in 2WD, and I've done all of them alone in the past too, if you can't find anyone to go with you. It's real obvious when you look at a map as to how to get there - just head north on I-15 to CA-79 South (it says Indio, but doesn't actually go anywhere near there) and then turn right left (the only way you can turn) on to S-2 (San Felipe Road). From there you have options depending on where exactly you want to go. Get a good guidebook - there are lots of things to see around here.
Blair Valley - I've been here many times, and have never needed or used 4WD. We did this as a 2WD-friendly club run last year in fact. There are some great hiking trails too.
Buttes Pass Road - if you stay on the hard-packed ridgeline route (Borrego Mountain Road on your map) to the top of the Drop-Off you should be fine. Certainly no problem to the parking area for the upper entrance to the Slot hiking trail, after that there are a couple of steep spots that could be problematic. I've seen passenger sedans at the Slot parking area. You might be able to also get all the way to Hawk Canyon, but there is a lot of soft sand along the way right now. I've seen VW sedans on Buttes Pass Road all the way out to San Felipe Wash. If you like moving fast through sandy washes, San Felipe Wash is an option too. You might want to have someone else along for that, or be good at self-extraction in sand just in case. Much of it is pretty hard packed right now though.
Check with the State Park rangers or there is a regularly updated chart just inside the door at the State Park Visitor Center that lists the trail conditions and what they recommend as far as 2WD vs 4WD.
[Edited to fix part of the directions.]
