I would recommend trying to spend as much time looking after the kid as possible. The more you look after them, the more rewarding they are.
I took 3 and a bit months off from 8-11 months and was a full time dad for those 3 months and it was great. Nowadays I work 4 days a week. If financially and work-wise you're able to do that, I'd really recommend both things; if you work long hours and don't get much time with the kid in the week, you miss out on all the weekday things, which are often quite a laugh (like we have Twistin Tots, which is basically an hour long baby rave, with loud music and different things to wave / bang / shake for each song, complete head-**** that is!), and the social things with other parents* which often happen in the week.
I agree about the outside stuff - Rose was running (in a pram) from about 3 months, biking (in a trailer) from 6 months, biking on a balance bike from 22 months, first time playing in the snow at 7 months, tons of picnics in the woods in her first year, decent length walks in the Peak District & Lake District in a sling, and she has always loved being outside. In some ways, particularly once they're a toddler and become self propelled, they are annoyingly slow and limit how far you can go, but I see it as a long game, you enjoy the time with them going 2 miles in a walk, because that is fun anyway, and as a bonus, you get the chance that at some point they will be fast and big enough to go on a proper outing with you. The bike trailer is brilliant though - you do 40 miles in hilly terrain with that in a day, and even with the playground / nappy stops & picnics, you still feel like you've done a pretty good bit of exercise.
Oh and swimming - swimming with kids is brilliant fun - we go a couple of times a week to the pool, and in summer we've been in the local river, the sea, a couple of big alpine lakes, she is a complete swim addict.
* other parents in the week are mostly mums, but that doesn't matter too much - I've always found everyone to be friendly, I think a lot of the stories you hear about dads not being welcome is people feeling shy because they were the only guy there. Or maybe it's a city thing, people are generally pretty friendly in our small town.