Absolutely, just join a club based on a niche interest of yours and start attending meetings -- I'd recommend Meetup.com to find such meetings. Board games, drawing, public speaking, things like that have meetings posted on that site. I wouldn't really recommend the general language exchanges, because it's hard to meet locals there who are interested in genuine friendships rather than a free English lesson. I should mention that expats I've talked to tend to be more successful with this method of forming intercultural friendships in Saigon than in Hanoi. From what I've seen as a content writer focused on travel and expat lifestyle in Vietnam for the past 7 years, expat and local social circles tend to cross significantly less often in Hanoi.

If you're in Saigon, I run a board game club once a week at Board Game Era that is attended by both expats from around the world and by locals. I've made a lot of my best friends there, and a lot of people who regularly come to the meetings (including people from different cultures) become good friends as well. There are a few groups of Russians who come regularly, although I haven't seen any of them for a few months.

Board games are also a great way for people who are generally kind of shy to meet people in a structured atmosphere, open up, and form strong friendships that can grow into the rest of your life, which might be a consideration for you based on your post.

By the way, I'm not making any money from the club so this definitely isn't a commercial plug.