Reddit reviews AC Power Adaptor for Nintendo Wii Console

I think a UPS is rather wasteful, as if you're running off a battery the UPS converts 12V DC (or 24V DC) from its internal battery to 120/240V AC...which then goes into the power adapter of the wii which converts 120/240V AC back down to 12V - at each step you lose a bit.

Much more efficient would be to hook up directly to a battery. The Wii needs 12V, so if you haven't got an LCD yet look for one LCD that also needs 12V so you don't have to bother with any voltage conversions. When buying the LCD, look at the power adapter that comes with it and find one which outputs 12V, or one designed for use in cars.

The next thing is to determine the size of battery you'll need. I'm not sure how much the actual draw is, but taking for example this adapter the wii will need 3.7A @ 12V. If you get a 3.7Ah 12V battery (3700mAh) then it will be able to run for 1 hour^. If you need to run it for 4, you will then need at least a 14.8Ah (3.74) battery to run the wii alone (look at sealed gel batteries which are common, cheap, and used in UPSes already)

^* Depending on battery type, you don't want to completely discharge it and voltage goes down as the battery drains. Theoretically you can get 1 hour @ 3.7A out of the battery, but towards the end of the hour it won't be delivering 12V anymore, therefore choose a battery bigger than what you need.