Since you arent printing, or need larger file sized images, and are just wanting to post to Facebook, relatively speaking, you'll be ok with just about anything.
I started out with a Panasonic Lumix point and shoot years ago before getting serious and becoming a wedding photographer. It was a great learning camera and did what i needed. Since you won't be shooting indoors and in low light, the above posters comment is irrelevant. Besides, most point and shoots suck in that environment anyway due to the small sensor.
Not wanting to plug the camera into the computer is fine, you can just remove the SD/CF card from the camera and put that into your computer/laptop, assuming it has a built in card reader (most modern ones do).
For your needs, you don't need to break the bank. I'd suggest looking into Panasonic offerings, read reviews, look at sample images, then go to BB and mess around with it.
Good luck!