I'm going to be out west for a few weeks and will be near some really nice trout streams. I've never been trout fishing, but would like to give it a shot.

No time to lear how to fly fish, and the little gear I have is heavy saltwater stuff.

I've been looking at inexpensive, short, 2-piece light and ultra light spinning rods and reels on a $40 - $50 budget, and it would be nice to hear what you guys recommend.

I"ve had really good luck with pflueger trion combos for ultra light trout fishing. For smaller streams i usually use a 4' 6" or a 5' rod. Those generally tend to be 1 pieces. I did a quick look on cabelas and I didn't see much in a two piece.

I usually fish something like this. They seem to have updated the line since I last bought one.
http://www.amazon.com/Pflueger-Microspin-Ultralight-Combo-6-Inch/dp/B001444SD6/ref=sr_1_12?s=hunting-fishing&ie=UTF8&qid=1410528074&sr=1-12&keywords=pflueger

These seem like descent options and come in a two piece.
http://www.fishusa.com/Product/Quantum-Xtralite-Spinning-Combos
http://www.fishusa.com/Product/Quantum-Teton-Trout-Spinning-Combos

Light line, light rod and small stream trout can be a lot of fun. Good luck.