looking for games

From your post I am assuming that your second gen Core i-3 processor has Intel HD 3000 graphics. Intel has offered this page as a listing of games you can play for reference:

Games playable with Intel® HD Graphics 3000/2000

One that I can attest to playing and beating with the IGPU with Intel HD 4000 (Core i5-3570k) is Borderlands. I played it at 1366X768 resolution with everything turned up to max other than one setting which was left off and V-Sync Enabled through the Intel Utility and the frames stayed in the 30-35 range but never dipped below 28. With the 3000 IGPU on your core i-3 I would think that 720p gaming on Borderlands would be acceptable with close to the same settings or turned down a bit. The GOTY edition is on sale a good bit for $10 or bundled for less.

You can also search YouTube to see what people are playing with the HD 3000 graphics. Some games I saw with a quick search were Skyrim, Battlefield 3, and Dues Ex. I would stick to Intel's list though as it should be perfectly compatible if you have the other system requirements met to play the games. You can also do a search for "system requirements lab" for an online "guestimate" as to whether you can play a game.