She only lives a few miles from here but she often has her power go out sometimes for a day or more.
So a laptop is great, it will work with the power off.
The problem is she would like to have an internet connection when the power is down
She needs to get a "good" UPS with AVR - automatic voltage regulation. With a decent size UPS (say 1000VA or larger) she can connect and protect her notebook and all her network gear. Of course, run time will be extended if her notebook battery is fully charged before the power loss, but she still should be able to run for a couple hours - longer with a larger UPS.
Most importantly, she will have power to send for help - if the power outage takes out her phones too.
APC is probably the best know UPS maker and for sure, makes quality UPS. You can't go wrong with a decent APC. Cyberpower also makes good UPS, and tend to be a bit less expensive than APC. You don't have to spend $400 on a good UPS (though you easily can), but you must avoid the cheap, entry level models. Like PC PSUs, there are cheap models/brands to avoid. They tend to have slow cut-over times, poor output waveforms, and lousy regulation. The better models output near sinewave power, provide excellent regulation (the "bread and butter" of a "good" UPS with AVR) and have a very fast cut-over times - and are more than capable in most home environments. The best, and most expensive UPS have "pure sine wave" outputs - and if budget allows, are recommended, though not absolutely necessary.
All computers (and big screen TVs and home theater audio equipment) should be on a "good" UPS with AVR. Not for the battery backup, but for the regulation AVR provides as surge and spike protectors are little more than fancy and expensive extension cords that hack up, clamp and obliterate the wave form during high voltage anomalies (surges and spikes) and do absolutely nothing for low voltage anomalies (sags - opposite of surges, dips - opposite of spikes, and brownouts - long duration sags). The resulting wave forms (if they can be called that) from surge and spike protectors are messes ("dirty" power) left to the various power supplies and regulation circuits on the motherboard and in the connected devices to (or attempt to) clean up.
Backup power during a power outage is only the "icing on the cake".
FTR, I have an APC 1500VA UPS that supports my wireless router, cable modem, two network switches, phone, and my Intel i7, 16Gb PC with a decent (read: power hungry) graphics card and TWO 22" widescreen monitors - providing at least 35 minutes of run time should power go out - 45 minutes if I kill one monitor and over 1 hour if I kill both monitors. If I power off my PC too, leaving just my network running, I get over 3 hours of uptime which I can use with my notebook running off the notebook battery. Now if only my notebook battery would run that long.