I was spending a lot of time on scales and exercises and found I wasn't progressing or having as much fun after a while. Like you, I decided I needed to learn a few songs to bring the fun back. It was a real break-through for me and now I add a song or two every week.
The key for me was just using the basic open chords and playing rhythm. Rather than just practicing the chords, when you do it while learning a song it just becomes that much more fun. Pretty soon you'll be able to play a song from first reading of the tab. It's been a blast for me.
With a little practice, you'll start moving easily between all the most popular chords: G, C, D, F (a little tougher - of course - but easier after a while), A, Am, E, Em. With those chords there must be thousands of songs you can play. Throw in a few easy variations like E7, A7, C7, G7, and Dm, then a few "sus" chords such as Asus4. All of these are easy variations to learn and they add some more colorful options to the songs.
I bet many of your favorite artists have songs that can be played in the open chords above. Just think of a song or two you really love and get on the net to find the chords/tabs. Look at a few varieties to find one that may be a bit simpler for you to play.
My list now includes Neil Young (Heart of Gold, Needle and the Damage Done, etc), Lucinda Williams (almost anything is G,C, D, etc), Beatles (Let if Be is a great and easy song), Van Morrison, Jason Mraz (I'm Yours is easy with a capo), and several others. I just added Alberta by Eric Clapton, which is a great easy and fun song.
A lot of people put House of the Rising Sun on the list. It's on mine now but the D to F change is not the easiest for beginners so I'd put it a bit further down the list, but then it's a good one for some basic arpeggio playing.
Finally, I don't know if you're into the blues, but I love the basic 12-bar form and get a lot of joy out of just strumming them in several keys. There are some good lessons on here if you aren't familiar with it. I can sit in my chair and just mess around with a blues in E (using E, A, B), or easier A (A, D, E) for hours. Even basic chords only are fun, but then throw in a few variations, vary your strumming, learn some base note walk-ups, a few easy lead riffs, etc. there's just lots of easy stuff to learn in here and then improvise while sitting on the porch with your dog and a glass of scotch (or whatever floats your boat!)
That's what got me over the first hump, but I'm sure I've got several more in my way. I've been playing for about 15 months now.
Hope this helps,
Bruce