You can take your baby (now 6 months) to any of the children's centre stay and play groups - there are some groups specially designed for under 1s. Your biggest local children's centre in N8 would be Campsbourne CC on Nightingale Lane.
My favourite baby group was at Downhills School in N15 on Tuesday afternoons - frequent 41 bus from Crouch End stops almost outside.
Lots of the libraries have something on and I'm sure Hornsey Library has stuff, pop in and ask.
Contact the Haringey NCT branch and find out if there are local "teas" where you can meet up with other mums (and even dads) for a tea and chat
There was a Jolly Babies group on Monday afternoons at Burghley Road Under 5s near Turnpike Lane - I've seen evidence that it was still going.
There are various classes and activities that you pay for at the YMCA which lots of people I know have talked enjoyed.
The Odeon in Muswell Hill and the Phoenix in East Finchley have screenings you can take a baby under 1 to - not necessarily aimed at kids but at their parents - I went to see two extraordinarily violent (but quite good) films at the Phoenix with my 2nd baby (never made it with the first).
There are music mornings in Priory Park but you have to pay.
Park cafes are nice places to just hang out with the baby, and you can take him/her to the playground - at 6 months baby might enjoy a gentle go on a baby swing, or just looking up at the trees.... my first was born in May and my 2nd in February so they were a bit younger in their first summer. Or you can take sandwiches and fruit, jars or suitable food for baby led weaning to the park and have your lunch there rather than in the house.