My electrical set up, complete, has cost over $10,000 and I can go off the grid for as long as I like. Obviously its crazy to invest anything like that for a weekend cruise. But if you look beyond some of the advice here that suggests you buy this and that, you might be able to come up with a creative solution that costs very, very little.
A bucket of water in the freezer at home on Monday, start just 1/4 full and each day add a bit, by Friday will be a block of ice that will last till Monday on the boat.
Instead of LED lighting have a look int he hardware store for an LED lantern. I buy them for $6 each, they have a torch at one end and a lantern in the handle. 3 AA batteries last 300 hours!
With your boat battery, instead of buying a whopper like I need you might be able to buy one that you can carry home and put of a $30 trickle charger. But will you need much of a battery at all? The depth sounder wont take much power, hand held VHF can be charged at home during the week and wont use much on standby... As for the AM/FM radio they acually dont draw much either (you could sing to yourself) but on the water and at night on anchor I prefer the silence and the sounds of nature. FM music can be butt shoved with glory!
Perhaps try some of the ideas like that, and creative ones you think up, for a few weekends and see what works and what doesn't and which ones you really, really, need to spend money on.
By the way, a fuel Hurricane Lantern puts out a warm glow, smells like a boat should and can really make a nautical experience...