I normally carry 3 lights that might fit your needs. On my keychain is a Skunk Lights Skylight solar rechargeable LED light. Not real bright but good for finding the keyhole in the dark and never needs batteries. On my small tool ring I keep a Streamlight Key Mate. This is about 2" long by 1/2". Very bright and runs on 4 coin cell batteries. Had it for a year or more and haven't changed the batteries yet. The last one goes along in my attache bag. That's Gerber Infinity which uses a single AA and is reasonably bright. It comes with a lanyard hole and pocket clip. All of these can be had for under $30.