Well, first off we need to know what your current battery is.
I've been alternatorless in the Paseo for a couple years now. I have a group 24 (~70Ah) lead acid deep cycle battery and it easily lasts 50 miles in summer driving (even with headlights on and wipers going). It cost me about $70.
If you go with lithium, CALB or thundersky batteries are much cheaper than A123. Quality is also lower, but IMO this won't be a problem in this relatively simplistic system you're looking to create (it isn't for most EV owners using these cells). Even still, a 60Ah 12V battery from CALB will cost you around $330 plus shipping. Now, this battery will probably last much longer than the $70 lead acid battery. It could possibly last the life of the car, or longer. Now, you also have to get a lithium battery charger. Some are as cheap as lead acid chargers, so its kind of a wash there. The weight you save will be in the area of 20-30 lbs. So, there are plusses and minuses.