I play the digital version of the game. The available zones so far are the City, Dungeon and Highlands. There are a ton of character guides online but I haven't really found a resource on the strategy behind the expansion zones.

For example, yes, the City is where you can spend gold to obtain items you need. But it is faster to grind strength/craft with the encounters there (or the other expansion zones) or on the normal board? Should I always aim to get gold and go for the power items in the City (ignoring the other expansions because they are slower) or are there specific situations/characters where the dungeon/highlands are actually superior options?

Can I get a brief overview of what benefits each of these zones provide and the strategic reasons to why and when you would attempt to enter each of these three areas (with the assumption that you are trying to win as quickly as possible)?

Dungeon - among 128 cards there, 100 are Enemies. Obviously You go there to grind stats, and steal Cloak Treasure card.

Highland in theory has gems... but frankly they are rarely appearing. But You get there a lot of trinkets, so Objects that do not count as objects. And the Big Bird there has the Arnkell - an Object You might want to get.

The City has a Flail. And a Bow. Nomads killed the Scribe, so it is not as useful as it was. Also there are some interesting Pet cards that can grant You auto win.

Can I get a brief overview of what benefits each of these zones provide and the strategic reasons to why and when you would attempt to enter each of these three areas (with the assumption that you are trying to win as quickly as possible)?

I was writing something about this just while you where asking. I'll cut and paste with min. amendments:

Dungeon, Highland and City offer different rewards and different levels of risk, which shall be learned by playing. Every place is worth a visit sooner or later, but only with experience you will know when’s the right time.

A character enters the Dungeon late in the game, when he wants to boost his already good stats by fighting lots of Enemies, with the ultimate goal of reaching the Crown of Command via Treasure Chamber (depending on the Ending used).

On the other hand, a character can go to the Highland at the beginning of the game, because the danger level is pretty much the same as (or lower than) the main board. The main reward there are the Trinkets, because they don’t take inventory room, and some are really good. Then, there’s always the chance of getting loads of gold with the gems, which is worthy if the City Expansion is used.

It is safer to go inside the City if you already have some gold to spend and know what to buy. Hoping to find it randomly is no safe bet, since drawing cards in the City goes at a slower pace if compared to other corner Regions. There are almost no dangerous Enemies there and concrete opportunities to get real good stuff if you have enough gold. It's not a place to increase Strength and Craft.

Highland: you can and often should enter as early as possible, certainly once you have gained a strength and/or craft and city enchantress stops being useful. Middle region is somewhat preferable if you can get there as it safer and fewer enemies but a few spaces into highlands there are several spaces that allow you to draw many cards and that's what you want generally.

Dungeon: you dont generally want to go there till you have around 10 strength+craft and even then you dont want to go too far in till you have closer to 16 total. Not all the enemies are powerful and there are some good objects, generally your risk vs benefit is higher elsewher, until you are so strong you will win most fights. once you get strength or craft to 10 its the fastest place to get it to 14 though.

City: enter only to use shops or the wanted posters at the gate (and use those when you can) the citycards are almost all pretty useless or effects random. if you have the gold to buy a spellbook or a flail you want to make your way here soon as convenient. The pets are also powerful but not quite worth the trip on their own unless you have a movement bonus.

one use for the city is that if you are low on life it's the safest region and offers some opporunities to gain gold so that you can heal.