Assuming you are already breaking it up into plenty of feeds and sleeps... I remember it feels odd, finding ways to entertain a tiny baby.
Have you got any of the black and white books to show baby? Or a black and white mobile for the cot. I think I had wrist and foot rattles at that age. Oh and it's never too early for a baby gym - choose one with plenty of dangly bits for baby to look at.
Lots of walks in the pram, especially as it's summer - the fresh air is great. Ditto lying on the grass on a blanket (under a parasol/tree/gazebo if the sun is out, babies that small really don't need direct strong sun).
I took mine to baby swimming at 4 months, so a bit to wait yet (some do start earlier but not sure how old) but now's the time to get your name down for a course if you're interested.
Baby groups are good - the church hall or Surestart ones are good, all you need is to meet one or two like-minded mums and you can splinter off for coffees by yourself if you're not a fan of baby groups. If you meet some other new mums you like, and you have them round to yours/go to theirs, the babies often love "meeting" each other on a blanket on the floor.
And definitely do a baby massage group - your baby is the perfect age to enjoy it and again, it's a good way of meeting other new mums. Ask your doctors/health visitors/sure start centre for details of baby groups. There is nothing quite like chatting with other first-time mums (if this is your first) with babies of the same age as yours, you learn all sorts of things and swap tips.
Also check the local library for anything like baby singing (the mums do the singing, the babies love the rattles/actions, even the tiny ones enjoy it) or story time, or anything baby-related.
Gradually you will build up contacts and things to do which slowly fill the (sometimes long and lonely) spaces in your day.
HTH x