In order for someone to benefit from your tapping a house or building, two things must happen:
1) The person must log in before the timer that you started runs out (please correct me if Im wrong, but I dont think the person will get any benefit if they accept the handshake after that timer has expired).
2) After accepting the handshake, the person must return soon after the adjusted timer runs out to tap the house again
because if they dont, the shortened timer didnt really help them.
For example, if I tap a friends pink house at 7pm, itll be ready again at 1am. The friend might log in at 9pm and accept the handshake (getting the same payout they would have if I didnt tap it), but assuming theyll be asleep, it didnt matter that I bumped up the next renewal time from 3am up to 1am. They still wont tap it again till morning, so it didnt help them at all. However, if I instead were to tap a purple house at 7pm, theres a chance that theyll be able to log in and tap it before 10pm to accept the handshake, and again after 10pm to benefit from the earlier purple payout.
Therefore, the strategy that is most likely to benefit your friend is to tap houses or buildings that have the longest duration such that it still results in the timer running out before your friend goes to bed. Or, find ones with a timer that expires around the time you think your friend will wake up (for "stranger" friends, I just assume they're somewhere around Central timezone). Also the 24h and 48h timers are always a good choice. Here's a helpful list of some of the longer interval buildings, put together by tsotips.com:
2 days: Burns Manor; Krabappels Apartment
24 hours: Duff Stadium; Pimento Grove; Springfield Penitentiary; Springfield General Hospital; Volcano Lair; Holiday Tree; Santas Village
16 hours: Fat Tonys Compound Phineas Q. Butterfats; Springfield Library; Springfield Observatory; Orange House
12 hours: White House; Hibbert Family Practice; Sprawl-Mart; Santas Village; Sleep-Eazy Motel; Mapple Store; Wiggum House; First Church of Springfield; Skips Diner; School Bus
10 hours: Asia de Cuba; Legitimate Businessmans Club; Howards Flowers; Springfield Cemetery; Springfield Pet Cemetery
8 hours: Swanky Fish; Springfield Coliseum; El Chemistri; King Toots; Jakes Unisex Hair Salon; Sir Putt-a-lots; Springfield Buddhist Temple; Blue House; Aztec Theater; House of Evil; Mausoleum; Super Collider