Sleeping Dogs.

Saints Row 2 was the best in the series for me and I recommend it. SR3 was way over the top and SR4 should never be mentioned again.

Sleeping Dogs.
Saints Row 2 and SR: The Third.

Sort of :
https://www.gog.com/en/game/total_overdose_a_gunslingers_tale_in_mexico

Others not yet mentioned:

Mafia Trilogy
Yakuza Series
Cyberpunk 2077?

Cyberpunk 2077

Like GTA, but with a heavy emphasis on sci-fi.

not the closest, but in the same vein:
Driver: Parallel Lines

Since no one has mentioned it yet, I would like to suggest The Saboteur.

Saint's Row 4 doesn't get enough love, but everything mentioned here have been good choices.

No, not at all. The cities in those games are nothing but backdrops. Sure you can theoretically drive around in them all you want, but there is literally nothing worthwhile to do outside of the story beats.

I enjoyed Just Cause 2. However, I'm not sure if you'd find it too over the top. You have a parachute and grappling hook that you can use to sort of fly around with. You also blow up a lot of stuff, can ride on top of cars, etc. It's a lot like an open ended action movie. Personally, I think that helps keep the game a lot more interesting, but I'm not sure what you'd like. It's on sale at the moment, so it's really cheap.

You could check out some gameplay videos to see if it interests you.

that's because it's not very good compared to 2 or 3

I wouldn't call GTA 5, nor any other GTA game, as being anywhere close to "semi-realistic."

Mafia 1, the original version from 2002, that's what a realistic or semi-realistic game is like. Although Mafia 1 has been totally butchered on GOG and therefore is not worth buying or playing the GOG version, unless you know how to and are definitely going to apply a mod that restores it to its original non-butchered version.

In contrast, all GTA games are nothing like that, and instead they are totally asinine and not the least bit believable or immersive or realistic; i.e. the cops totally ignore you if you speed or run ride lights or drive in the opposite direction of traffic, etc. etc., while you are right in front of them.

Sleeping Dogs, as has been mentioned in this thread, is similar to GTA in some ways, but also asinine and totally unrealistic & unimmersive in exactly those same ways that GTA is.

"Mafia Trilogy" was also mentioned in this thread. Except that only the original Mafia is realistic, and the later games are dumbed-down and trashy just like GTA. In other words, Mafia 1 original version is in no way comparable to Mafia 2 or Mafia 3 or Mafia: Bad Remake Version.

Seems they've been listed prior but I'll say (again)...

Sleeping Dogs -- great story-based open world game but not a lot of mini-games (a few)

Mafia trilogy -- great story-based open world games with very atmospheric cities, but almost nothing to do in them other than story and sight seeing.

Saints Row 2 -- open world mayhem in a somewhat grounded setting (this is where SR started to get kooky)

Yakuza series -- story-based small open world (traveled mainly on foot) with a lot of mini games and arcade beat-em up combat mechanics


I'd guess you'd connect most with either SR2 or Sleeping Dogs, but if you want great story Yakuza or Mafia.

Not that anyone asked me, but I'd rank them:

1. Mafia trilogy (with 3 being not lesser of the 3)
2. Sleeping Dogs
3. Yakuza series
4. Saints Row 2