It would be mainly set in a High School.
A new "British" girl (ie cringey fake accent) would have started at the school, and everyone would tease her for being "ugly" and "weird" and having a very British name (Susie), despite the fact that she was played by some token cute blonde, and was full of cool pop culture references, quick "witty" one-liners and a - shudder - "sassy" attitude.
The school's main jock, Ian, and his cheerleader girlfriend Vicki (played by some of the weird interchangeable plastic-faced twenty-somethings off of all those interminable CW shows) would tease Susie a lot for being ugly and not sassy, and one day would chase her to the janitor's room, unaware that her Grandfather (who she would henceforth call "Pops" because f*** us, right?) was the school janitor.
In the janitor's room they would discover the TARDIS, which looks like a Police Box because the execs making the show think that this is what every TARDIS looks like, and meet The Doctor (Charles Dance in the sole British piece of casting). Before you know it, aliens are invading the school, and Susie [who, incidentally, gets top billing in the opening credits, which play over an electric guitar version of the Who theme - Charles Dance gets the "And... As Doctor Who" at the end of the credits] takes them on, with Ian and Vicki reluctantly in tow.
The four turn out to be quite the team, even though Ian is comically stupid and serves as the punchline a lot of the time. Vicki turns out to be not quite as much of a bitch as cheerleaders are supposed to be according to television, and becomes torn between her new friend Susie and her old head-cheerleader best friend (who is always kept in the dark about the gang's "secret", and, wearyingly, is also in the opeing credits...).
Most episodes take place in and around the High School, which is "amusingly" referred to as being in New England as a clever nod to the show's origins, but in reality looks like it's in California. The TARDIS is mostly used as a base of operations for the gang, where they gather to discuss the threat-of-the-week with The Doctor, who sends the kids off to fight in his place most the time and serves mostly as a mentor. Trips in time and space are reserved for "event" episodes.
By mid-season there'll be a love triangle between Ian, Vicki and Susie, The Doctor will have a "charming" awkward and bumbling relationship with the school's foxy middle-aged principal, and millions of American fans will loudly and obnoxiously declare it to be far superior to "the old version".