This post contains SPOILERS and is destined for meta gaming aficionados. Don't read it if you haven't finished the game yet and want to discover things by yourself as one should in my opinion.
Early Constantine's : Play as a female character, accomplish Jack Quicksilver's questline as soon as you get the drill parts by convincing Delma to allow you to talk to Todor without going through the Beast quest.
Fraser's shop: Do the Rail Crossing 1st quest (maybe sacrifice Buzzer*...) and get the Train Heist. Side with Protectorate (you don't have to fight, reporting the train to the SRO is enough). You have access to Fraser's now.
Dude's juice: If you've unlocked Fraser's, buy Omnilube and accomplish Dude's quest. The only enemy you need to take care of / pass by sneaking is a sentry bot for the first quest. For the second, it is solved as usual except the last part I think, because you can just use the Omnilube (didn't verify myself yet, but it's been implemented I think). Incorrect, see below.
Expedition: Through Beast fight or Train Heist (but I think one should resolve the quest by force for it?), you have access to Black Sea by being recruited at Core City docks. Survive the first assault through bear traps and caltrops and hiding yourself courageously.
Hypercerebrix, Plasma Beam, Third Eye, Twitch, Lemurian spear: You need to get Phil's arm, but once you do, you can just pick into the pocket of the technician for the Talkie and denounce him, follow instruction and go take a nap (in the game!). The path to the entrance of the Citadel of Life is now opened to you. You need to cheese the 4 nagas, but it can be done through stealth and luring them in a corner with tnt, I believe. If you don't have pickpocketing, just join the Pirates.
Benches: Coretech questline might be the easiest, especially the warehouse defense that can be done through the use of Gas Grenade and waiting in the exterior of the warehouse by the window (same screen). The warehouse mission after Cornell is easier as well since robot won't attack you and Death Stalker can be dealt with noise and snails. Just don't get ambushed by Tchortists if they are too strong for you by leaving the warehouse by where you've entered it.
What are your tricks and tips on unlocking things faster?
*You can save him by doing Hugo's quest at Foundry first and solving it through money or with poisoned caltrops and noise.
