Hi.
Try social sports clubs.
There will be loads of these in a big city, and you may find that the people who are into sports are a different crowd to those who are in the bars late at night.
Another benefit of sports is that the experience is structured, and the focus is primarily on the activity, rather than on sitting around talking. This is a plus if your conversational skills are like mine!
There are less-or-more competitive grades, so even if you are not experienced you can fit in somewhere.
Although it requires some bravery to join in at first, most sports are welcoming to new members because they need people involved to make the game happen.
Sports generally involve between one and thirty players, so there is choice of group size, and physical contact.
The teams often socialise after playing, or at other times during the week, which gives you an "in" to a social group.
Mixed teams are popular these days too, so there is opportunity to meet women as well as men.