This is something I've been thinking a lot about lately, since the achievements in Witcher 3 (Steam/GoG version's) are currently broken and so much as mentioning the issue on forum's turn's into getting lectured by others about how achievements are the devil and how they're ruining gaming and that you should feel bad for caring about them. So, I'm glad you brought it up because I've been meaning to have a serious talk with other gamers about the subject.
My stance is that caring about achievements is not a bad thing at all and you definitely should not feel bad about caring about them! Achievements can add replayability to a game that would otherwise have little to none (ex. South Park: The Stick of Truth), they can add extra side challenges to a game that you would otherwise not think of doing (ex. Orc's Must Die, Portal, Goat Simulator), make you play the game in a completely different way then you normally would have (ex. Civilization) or simply make you explore area's that you might not have known were there/might not have cared were there (ex. Skyrim). They can help you feel a sense of accomplishment and help you feel as if you've truly completed a game more then simply playing through the main questline. I'm going to be honest here, there are a number of games that I would have stopped playing upon completing the main questline if it weren't for achievements and I'm grateful for that because it stopped me from rushing through some games that really shouldn't be rushed through (ex. Bioshock 2 and Bioshock Infinite).
You're not any less of a gamer for caring about achievements and I'm about to say something that might piss a few people off but if achievements were around when I was a kid, playing through Super Mario Bros. 3 or Zelda, it would have made those classic games we all love to remember that much better (and I'd be able to finally provide proof that I kind-of-almost-oh-who-am-I-kidding-this-never-happened beat Battletoads).
It doesn't make you any less of a gamer to care about achievements. In fact, in some cases, I'd even say it makes you that much more of a gamer (Dark Souls is hard enough, 100%'ing the game and getting all the achievements? That's badass). It doesn't mean you're part of the reason the gaming industry is being destroyed (despite the fact that gaming culture is at an all-time high but that's a topic for another time). You don't need this talk. You're free to enjoy gaming however you want to enjoy gaming even if that means you pass up playing games that have no achievements. Personally? I'm okay with playing games that don't have achievements but if they do have them they better fucking work! CoughCoughWitcher 3 (PC)Cough*. My bad habit is that I prefer games with achievements to be on Steam because I like to keep all my achievements in one handy place. I mean, of course, if you don't play games that have no achievements you're missing out on some pretty great game's (Fallout 3 - PC for example) and if I could pep talk you into thinking that it's okay to play games for achievements but don't skip out on a game just because it doesn't I would but it's your decision how to enjoy games in the end. No one can make that choice for you.
As far as your run-in with Cities: Skylines, why not playthrough the base game and get as many achievements as you can before adding mods? It will make adding mods more rewarding as it can only increase the life of the game for you. That's kind of what I did with Skyrim. 1/3rd of my playtime in Skyrim was in the base game (typical OP archer thief build to collect all the achievements), the other 2/3rd's were when I started adding mod's. I have no regrets. I'm not too familiar with Cities: Skylines though.
TL;DR: I think the hate toward achievements in games and the people who enjoy getting them is ridiculous. The people causing players that enjoy achievements to feel bad about themselves need to stick their head out of their asses. If they don't like achievements that's fine but there's absolutely no need to try to be a dick or try to change other peoples views about them.