Well, if you checked the prices for 1kVA UPS that can hold for 2h, you are looking at price tags in the $1300-3000 range. You would be better off buying a $200-ish UPS for your modem+router and a laptop or/and tablet for your down-time browsing/gaming needs.
When I get hit by a power outage, I put my computer into hibernation, load a bunch of pages to read on my tablet, shut down the UPS and hope power will come back before I am done reading.