Strategic? Would a tower defense game fit that genre?

Well, my personal favorites inlclude geodefense, and geodefense swarm.

These games a very challenging, rewarding, and highly addictive. I've beat both of them multiple times and you got to trust me when I say they require a lot of strategy. I've tried many tower defense games, but for some reason these are the only ones I really like.

As for RPG games, I would strongly recommend Chaos Rings.  I haven't tried eternal legacy, but you may also want to try that game.

I'll just throw in some other suggestions that I really really enjoyed:

Enigmo, Ragdoll Blast 1 &2,  Flight Control. 

Some good suggestions made so far. Heed the warning about Eternal Legacy, though. I tried that game and I felt robbed.

Chaos RIngs or Crimson Gem Saga

Jailbreak it and have all the games you want.

But if you do this, at least try to pay for the games that you really like  later on!<_<! most of the games are from indie developers, and they deserve money for they hard work! :( I havent done it myself (I have the newer ipod touch) but sometimes i feel robbed for some of the games i download.

Oh and play Game Dev Story :D!!!! one of the best sim games outthere, and made for gamers like us!

Chaos Rings, even if it IMO, looks ugly on 2nd gen.

Nope.  Legit gamer here.

I wish Chaos Rings was on Android.

By the way, grab Zenonia and Zenonia 2. Excellent titles!

Also worth mentioning if you like games with an RPG style is Baseball Superstars 2010 and 2011.

You only really need to hit and you get to work on stats and shit and it is a great pick up and play game.

Should have a demo for every title I mentioned other than Chaos Rings.