Add batteries plus an inverter. Even if you end up doing solar (not advised in your case), you'll still need more batteries and an inverter.
Next step is a power audit. Add up the power requirements of the stuff you use at night and see how much battery you need to make it comfortably through the night. Figure out what your peak power use on battery will be, and get an inverter big enough to handle the load.
A 7k Honda is a honkin big machine, and a 2k Honda is not an unreasonable purchase. But wait a bit, figure out what your daytime peak loads are and whether you really need all that much power for a weekend camp. Then size your smaller gennie to fit that--although the 2k Honda is certainly a great choice.
