Very similar to what @IamnotwhouthinkIam said: diminutives, lots of names with -ie, -y or -ee endings, but not more cosmopolitan French names like Sylvie (I do however find Amelie quite twee), or Greek origin names like Xanthe, Zoe or Daphne. Also a few exceptions like Nancy, Josie and Holly, which I feel have a bit more energy to them - to me part of the ‘twee’ feel is being a bit weak and insipid.
Maisie
Daisy
Posy
Elsie
Rosie
Gracie
Connie
Kitty
Betsy
Lottie (a pet hate of mine!)
Ellie
Emmy
Millie
Evie/Edie
Most ‘cheeky chappy’ boys’ names ending in -ie (but not Laurie, which oddly is one of my favourite names!)
Alfie
Albie
Teddy (and Bear!)
Sidney
Freddie
Archie
Also obviously frilly, princessy names - things like Arabella, Arianna, Aurora... There are lots of girls at local toddler groups with vowel-heavy, slightly made-up sounding names ending in -ana or -ella (Caliana, Ariella) - all of those.
Cutesy nature names:
Primrose
Blossom
Luna
Also find Arlo and Milo quite twee for some reason.