Note that batteries will cost as much as the light potentially, which makes your request impossible.
Do you already have an AA battery charger by chance? If so, this reduces your costs and Id highly recommend a good AA flashlight.
Do you have an 18650 charger? If so, go that route. A 1x18650 light such as that XTAR is a great choice. There is also an MG light that is sufficiently bright as well.
If you have neither charger, I would go the AA route personally. This is because you can use AA rechargables for other electronics, whereas an 18650 is fairly worthless. For 30 bucks, you can get a nice eneloop pack with 8xaa, 2xaaa, and a charger. Not bad!
For lights, this is tough. You will have to up the budget. A 2xAA light is ok, but you just wont get that kind of lumen output. There are no 3xAA, 4xAA lights since the form factor isnt very appealing. (with a few exceptions).
I'd go with an itp A6 Polestar. 80 bucks (minus 10% discount at goinggear) with free shipping is what I did for my dad. It is relatively small, claims 700 lumens (probably closer to 500), has 3 useful modes and a holster. Its pretty floody but you can certainly see stuff at some distance; good enough for most people.
