I have the quests There Stands the Grass and I Could Make You Care.

There Stands the Grass has the following objectives:
-(Optional) Find Keely
-Download research data

I Could Make You Care:
-Recover the experimental data from Vault 22
-Return with Veronica to the BoS with evidence

I have gone to 4 of the 5 floors, and haven't found any of the objectives for either of the quests. Can somebody help/guide me?

Forget Keely and just go for the data. The data is in a small room with a big mainframe with a terminal on it down in Pest Control. Just activate it and select the option to download it; that satisfies both quests.

Go to the commons floor and look for the Overseers office in there you can access a computer to unlock the door to the computer that has the data you need.

Kelly is in the cave system that is on the Pest Control floor, after you find her she goes to the second floor then tells you to ignite some gas on the 5th floor, for that just toss a grenade into the gas then go into the room with the computer you downloaded the data from earlier and close the door, you'll still be hurt but it should'nt kill you.

Is it in the cave in Pest Control? Because I can't find a terminal with a big mainframe in any of the rooms on that floor.

It's not in the cave its in a room to the left of the dead-end where you see two vent openings, its on the other side of a hard-very hard locked door so if you don't have the skill go unlock the door from the Overseers office computer.

Oh I found it. Thanks!