Our take:

What! Tenchi's Moving To Tokyo!?! When Tenchi moves to Tokyo the whole house falls apart! But Thanks to all of Washu's inventions Ayeka and Ryoko can feed their addiction..... Tenchi! When Tenchi Moves to Tokyo he meets Sakuya, who ends up being Tenchi's first love, which causes some trouble with Ayeka and Ryoko, not to mention everyone else! But what no one knows was the that the house falling apart was not a coinidence, Yugi a evil girl from Jurai wants to destroy the earth but Tenchi's neckless forms a sword more powerful than Yugi's, so Yugi needs to separate everyone to weaken the crystals. Ryoko goes to space after seeing Tenchi and Sauya kiss, Mihoshi and Kiyone get re-assigned, Washu stays in her lab, Ayeka stays at home, and Sasami plays with Yugi, but she doesn't know who it is.

"What happened Tenchi!? Don't you like me anymore!? Is That Why you're going away!?" - Sasami (NA Dub)

Complied from the Pioneer Animation Web Site:

Tenchi Masaki leaves the country to go to Tokyo and to train to be his grandfathers successor as a shrine master. Of course, the girls can't be quiet about their abandonment! Thanks to Washu's new invention, the interdimensional tunnel, a long distance family life starts. Meanwhile in Tokyo, Tenchi is approached by a cute classmate, Sakuya, who doesn't know the risks of being Tenchi's girlfriend!

While Tenchi enjoys his new life in Tokyo, the girls back at home experience a financial crisis! They resolve to get jobs in Tokyo to earn money, but can the easily distracted and excitable alien girls really hold down a job? Can Tokyo even survive their attempts?! In any case, you can be sure the mysterious and malicious Yugi will make their lives as difficult as possible...

Tenchi returns to his hometown for the anniversary celebration of the arrival of the alien girls. However, when Sakuya follows Tenchi home, Ryoko and Ayeka almost turn the party into a war! The situation only gets worse when all the alien girls' crystal pendants disappear shortly after Sakuya arrives. Who is the real thief!? Later in a suburb of Tokyo, an old ruin is discovered and Tenchi and his friends fall into a cavern beneath the ruins. There, they discover an empty 3,500 year old sarcophagus, and two hostile Jurai Guardians looking for the contents!

Yugi slowly builds her plot to divide Tenchi's group and bring her devious plan to fruition. First Ryo-ohki is seduced by another cabbit and taken to a colony of cabbits on the moon. Then, a stupid, love-crazy dopleganger of Tenchi's father tries to bring Tenchi and Sakuya together by kidnapping Sakuya. Then Yugi attacks Ryoko and sends two of her agents to protect Ryoko and to earn her trust. With everyone's loyalties going in different directions, will they be able to withstand a future onslaught?

Nothing can come between Sakuya and Tenchi. First, when Ayeka and Sasami try to hitch-hike to Tokyo, Yugi arranges for them to meet up with an aggressive woman on a motorcycle with an obsession for an impossibly fast jogger. Then, when Tenchi's friend Amagasaki threatens to break up the pair's romantic mood with interruptions, Yugi sends a spirit in the form of a professional female wrestler to intervene. Finally though, it is the bumbling nature of Ayeka, Mihoshi, Washu, and even Ryo-ohki that drives Tenchi to protect Sakuya from them when they accidentally destroy half of the culture festival at Tenchi's High School!

When Ryoko catches Tenchi kissing Sakuya, she becomes so distraught that she considers a return to a career of piracy! Meanwhile, Kiyone and Mihoshi are promoted to headquarters and Washu becomes obsessed with her research. Feeling alone and abandoned, Ayeka and Sasami attempt to bring the Masaki household together, but will Tenchi be too involved with Sakuya to care?

In order for the Galaxy Police to locate Ryoko’s secret hideout, Mihoshi and Kiyone have gone undercover to infiltrate Ryoko’s gang of pirates. But instead of arresting Ryoko, Mihoshi and Kiyone try to find out what Ryoko really wants and to see if there’s any hope of reforming her. Back at the Masaki residence, Washu has finally come out of her laboratory. She sends Aeka to investigate some ancient ruins to discover the true nature of Yugi. They find out that Sasami’s playmate and the one that attacked them earlier are the same Yugi. Meanwhile, Sakuya has taken up photography to capture the memories of her and Tenchi enjoying their summer vacation together. But their happy days don’t last long as Sakuya’s mysterious past begins to haunt her.

Heartbreak and Conflict! Washu discovers Yugi’s secrets and reveals them to a stunned Tenchi. Tenchi rushes to Sakuya’s where he discovers Yugi and her crystal fortress. Tenchi is joined by the rest of the Tenchi “Family� to confront Yugi, but Tenchi must enter Yugi’s crystal fortress on his own. Will defeating Yugi mean the end of Sakuya?!