Smartphone Bleg

My smartphone is dying.  Every other time the touchscreen doesn't recognize my finger when I'm trying to answer a call, the app store is broken, my browser has slowed to 14.4 kbps dial-up speed, and the cursor goes haywire most of the time I try to type something in.  I got it for free, refurbished, 22 1/2 months ago, so I'm trying to hold out for 1 1/2 more months so I have more selection (i.e. no longer tethered to my current provider, AT&T, for fear of early termination fees).  Since I'm not very savvy about these things, this means I am now actively shopping, as it will take about that long for me to pull the trigger.

I'm not sure if my smartphone's limitations have influenced me or not, but I find I don't actually use it for as much as I thought I would.  Again, maybe this is because I can't or because it's slow.  But also I think it's because I've compartmentalized my life fairly rigorously, so the portability that is required of people who like to do thing in an untethered manner is not nearly as important to me.  If I want to watch a video or bang out a blog post or coordinate my schedule, I don't feel a need to do so on demand.  Also, I don't play games, I don't scoreboard-watch, and I'm not a consumer of the latest songs and shows, so not having all of those things as readily available in my pocket hasn't fundamentally changed my daily routine.

That said, I would like a phone that actually works.  So I welcome your suggestions.  Amy's also with AT&T, but in 1 1/2 months we'll be free agents.  She likes her iPhone but needs a new one, and I'd like to stay with Android and pay as little as possible.  Any thoughts?  Any deals?  Any smartphones to avoid?