After I finished tutorials and quests in Arroyo, I headed to Klamath' but after coming to the city, I couldnt access it, global map just doesnt change to local one. The same situation was with every other city in game, even with Arroyo, after I left it, I couldnt return. Is there any possibility to fix it?

This is the general forum. Which game?

Try the Fallout forum.

The only things I can think of is;

Have you tried to click twice on the same marking when you come within the city limits?

Tried restarting the game and start over?

Vanilla or with mods? Tried Fallout Restoration Project which includes fixes for A LOT of bugs:
https://github.com/BGforgeNet/Fallout2_Restoration_Project/releases/tag/v26
Or at least the unofficial patch: https://github.com/BGforgeNet/Fallout2_Unofficial_Patch/releases/tag/v26

Can't say I have ever encountered that one...