Well, I came in here to post links to knitty and knitting help, but I’ve been beaten to it! I love knitty; their patterns are so much fun, and the articles are really interesting.
There’s also Magknits, and there are many millions of free patterns online – if you have the time, you can find all sorts of great stuff.
I have Stitch 'n Bitch, and while I use it for reference, I haven’t made any of the patterns in it. Last-Minute Knitted Gifts is wonderful, though, and I know that you could find some simple felting projects out there (maybe not for a summer project, though!). Try the Sophie bag at Magknits.
I think the first thing I made after learning was a shawl, because I’m in a knitting group at my church. Since then, I’ve just gone all over the place in terms of learning. Knittinghelp.com is fabulous, because it has free videos that you can watch over and over while you learn how to do a new stitch. What I did when I was just learning was make sure that my next project had 1 or 2 things that I didn’t already know how to do, and that way I was expanding my ability. Now, when I go back and do some of those patterns again, I may not remember exactly how to do that fancy stitch series, but I know where to find out, and it comes back pretty quickly.
Another thing you might try – Knitting on the Edge and Knitting Over the Edge, both by Nicky Epstein, are gorgeous books on edge knitting. If you want to branch out but don’t want a huge project, you could try a scarf with some of her edge treatments. Once I finish up the 4 projects I currently have on needles, I think that’s what I’ll be doing.
Oh! There’s also a knitting forum at Knitter’s Review. They’re great for specific knitting questions, and finding patterns, etc. Generally a pretty high-quality board, like this, with good grammar, spelling, etc. – which makes the experience a lot more enjoyable for me! The site also has great yarn and product reviews.
Here’s a fun project that I just made for a new baby: knitted bunny (I made it bigger than the pattern calls for).
There’s just so much out there! Isn’t it amazing, the things we can make from a lump of yarn?