1) “The Republic of Sarah”(shown here) debut, 9 p.m., CW. The quiet, autumn beauty of a New Hampshire town is pierced by the arrival of heavy equipment. For Sarah and her friends, life is suddenly transforming. “Republic” gets halfway through the hour before its plot starts to kick in; it also toys with assumptions about Sarah and Billy and others. Stick with it, surprises and all, and you’ll be rewarded. Its villains here are absurdly overdrawn, but Sarah (newcomer Stella Baker) is immensely likable.
2) “Celebrity Dating Game” debut, 10 p.m., ABC. Fresh from the second “Bachelorette” episode, we see a familiar face – which the guys who are wooing her don’t see. Hannah Brown has been the “bachelorette” … and been on “Bachelor” … and on “Bachelor in Paradise” … and is still looking for love. On this show, guys don’t know who their maybe-date is, but Michael Bolton sings some musical clues. He also does that for Nicole Byer (“Nailed It”), with other guys. Zooey Deschanel hosts.
3) Olympic trials, 8-10 p.m., NBC. Don’t look for “American Ninja Warrior” tonight … or for a full, two-hour version of “America’s Got Talent” on Tuesday. For now, NBC is all about the trials, deciding who will be on the U.S. team when the Olympics start July 21. It’s swimming this week, with track & field starting Friday.
4) Comedies. Here are good ones, back-to-back. A “Bob (Hearts) Abishola” rerun (8:30 p.m., CBS) finds trouble, when Abishola’s long-separated husband arrives from Nigeria. And “Housebroken” (9 p.m., Fox) reminds us that a raccoon doesn’t always fit into a group-therapy session for pets.
5) “Ms. Fisher’s Modern Murder Mysteries,” any time, www.acorn.tv. With its cheery, 1960s look and breezy attitude, this show is always fun. Tonight’s hour (the third of eight this season) is more serious than most: A murder takes James – a good cop and Ms. Fisher’s ex-boyfriend – back to the estate that denigrated his family. Also today is the fifth of six “Whitstable Pearl” mysteries: A mother takes her daughter on a boat ride, despite the father’s wishes; they soon need to be rescued.