Engineering - Mine - On the far left after beaming in is an NPC who sells them, they are close to the tailor contact.
Science -Embassy -(No Field Gens) - In the shuttlebay, the console on the right down the first ramp is for ship consoles. (The console in front of you after entering the shuttlebay and going down the ramp has some devices.)
Tactical - Spire (not in game yet.)
If you want more engine power I suggest using a fleet core that boosts Engine power levels via either X->E or a Hyper Injection core that buffs base engine power and get that way you can get armor that buffs your turn rate or turn consoles that buff armor.
Man is a gaming animal. He must always be trying to get the better in something or other.
Warning, this poster tends to talk nonsensically when caffine levels fall below 80%.
Tactical consoles: I don't think there are any, some are coming out with season 8 and the spire fleet holding.
Science consoles: Embassy, several types are available, including ones that provide a plasma proc. I think they are located in the shuttlebay.
Engineering consoles: RCS accelerators (turn rate) and armor is available in the fleet dilithium mine, a ferengi at the side of the room sells them.
Consumables: Some ground consumables are available in the Embassy, in the shuttlebay again.
Hope this was helpful!