I have an 03' tacoma with rear wheel lock so when one wheel is stuck they both spin and not just the loose wheel. I was wondering to what extent will my truck be able to go off road, like will it go on the beach or what
It will do fairly well stock. It will handle light trail duty. From the looks of your pic you have the stock all terrains. They will have a hard time in the mud. The beech should not be a problem. If you get stuck, do not lock up and floor it. You will only dig the hole deeper. Put it in low and try to crawl out. If that does not work break out the strap and have somebody pull you out, or get out the shovel and try to dig out the area in front of the tires and use the dirt to fill in the hole under the tire. Stick to designated trails in appropriate areas. Never wheel alone.
I took mine out on the dunes 100% stock and it did alright. I only got stuck once and that's when I slid off a dune into a juniper tree. Usually you can get un-stuck in the sand with low range or rocking it. You'd be amazed the places a stock TRD Tacoma can go. Just don't try anything too crazy without another truck around to pull your stuck truck out.
Oh, just read that you only have 2WD. The locker will help, but you'll probably have some trouble in soft sand. I'd only go out on the dunes with another truck unless you can stay on the wet packed part the whole time.