First off, fighting those four BoS Palidins that confront you after Veronica's was intense...... My level 11, 2 endurance, Energy Weapons using, no-armor character was about as poorly built for that fight as possible. (I pulled it off by eating like 8 Jets 5 Med-X's and 4 stimpacks before the dialogue box, then just blasted with the AER14 in vats as much as possible. BARELY survived.

Anyway- regarding Veronica's quest, she gives you three vaults to explore, I only explored one(I really didn't feel like doing the radiation vault at such a low level), got the data and went back. The quest was resolved but it wasn't a 'good' ending- I was wondering, if you go collect the items from all three vaults, then conclude the quest, does it have a 'positive' outcome? Instead of the boss rejecting Veronica's ideas?

Yes that was. Luckily, I had the C-Finder on me and I blew the Brotherhood up in one shot.

I hate that radiated vault. Many times I had to leave to heal my radiation. The only thing that happened to me in that quest was I got good rep with the Brotherhood. The head honcho trusted me and I received a key for the Brotherhood safe house which had nothing in it. I don't recall anything significant unless I missed something.

From what I can tell, there is no "good" ending where she gets her way with the Brotherhood. It doesn't make too much difference which item you take back, afterward you get the choice to either tell her to stay with the BoS, leave them for good, or make her own choice (she will prefer to stay). In either case where she decides to stay, you get the big nasty fight unless you can pull off the 95 speech challenge, and she stays with you from there on out. If you tell her to leave, she asks to go join the Followers of the Apocalypse, which leads to another big fight down the line.

Outcome: Veronica is unable to go in, but she will wait outside while you go in when her quests are complete.

Completing the Brotherhood quests nets you Power Armor Training, a BoS Bunker House of your own, a chest which refills with various energy ammo, and access to the Store and other parts of the BoS bunker.

I always assumed that Veronica's "I'm leaving" dialogue was referring to her leaving YOU. Thanks for clarifying.

Don't forget to get her a dress >.<

She teaches you a power move if you do

She does? What dress? I gave her [censored]loads of dresses (prewar park stroller/casual/etcetcetc) and while she commented and thanked me, I never got another move...

Has to be a highly classy dress, there is only one place in the whole Mojave region with upper class dresses and suits

I will let you guess where

She wants a real designer dress

The only ones meeting her approval are worn by the White Glove Society.