I don't know if this is helpful or not, but when I moved here two years ago I didn't have any friends here and I was dreading it. I went to four or five different toddler groups and was in tears at one because it just felt like I wouldn't ever make friends. I also find it hard as I have face blindness to a certain extent so find it hard to recognise people I meet when I see them again (usually work it out by the age/ gender of the children they have with them!). But some of the ways I met people were:
Saw the lady who lived across from us at softplay about a month after moving, chatted about our move, learnt they had a similar move, went round for playdate, reciprocated, DS ended up at same nursery as their DD. Had quite a lot in common, got on well, so friendship has evolved into going out without kids, family BQs etc.
Through that couple met two other nice couples (first at children's parties, nursery drop off etc) with similar aged kids who we now see with and without kids, the men sometimes go to gigs and the women tend to meet up every so often for a meal.
Went to NCT coffee mornings, the lovely organiser introduced me to loads of people, some I have become friendly with, going on trips, dinner parties etc, others just to say hi. Also through that lovely lady I joined a book group which has also been brilliant for meeting people.
Now DS1 is at school I have become friends with some of the mums there, not loads but one or two, one is the very friendly mum of his best friend and one I met at a toddler arts group and we got on well.
I hope this doesn't sound boasty look at all my mates, I just wanted to show how it happened for me, if it is annoying just ignore.