Where to work (remotely) with a 6 month old?

Almost any town that isn't remote.

You have to decided what you want... beach (not cheap food), near beach, up on a mountain where you can 'see' the beach..., or inland... where the possibilities include mountains, valleys, and of course, even suburbs and big busy towns. 

You don't have to live 'remote' to experience authentic Tico country life (farms, nice people, interesting wildlife; sweet friendly villages and small towns, and cheaper food due to the availability of fresh produce and such).  Example:   San Carlos canton (county) is huge.  It is in the north and offers a variety of landscapes and elevations... with valleys, rivers, mountains, and even some great 'attractions' like touristy La Fortuna... where rainforests and natural thermal 'hot water' rivers, and waterfalls, etc., are easy to find.  The city of Quesada is the capital of San Carlos... and has everything a small city would have anywhere... but the area is plum full of small towns and villages, from up high where you live in a cloud, to down low in valleys where it is plush and tropical... and so so much to offer; and generally, good Public Transit and regional buses.  It is the 'dairy' part of Costa Rica... and produce, dairy, and MEAT, tend to be reasonably priced and very available.  The city of Quesada is somewhat 'rich' but not pretty... the rich agriculture of the area has served the area well.  Nothing to see German autos and very well-dressed women; private schools, and even handsome Footballers... Quesada has a national soccer team too!!  German 'roots' are common there... so don't be surprised to see tall blonds with blue eyes; and even red-headed folks with deep Spanish roots to Galecia in Spain.

You don't have to live 'in' a big busy town or small city to enjoy what a place like that has to offer ... you can live just outside of one... in a 'fringe' neighborhood, or even a neighboring smaller town/village.  Most big population centers have public transportation; and smaller cities even have public transit within the city.

Perhaps look at San Isidro - General (known as Perez Zeledon) in the south of CR... which has the tallest mountains in CR to the east; and the south pacific beaches to the west. 

Or... try busy San Ramon... about 45 minutes west of the Airport (in San Jose burb of Alajuela)... which has many neighboring villages and towns at various elevations.  Pretty central park, good shopping, cheap clothing for some reason, etc.  Has a hospital; clinics, everything you need.  Excellent regional buses to neighboring towns; and almost hourly buses to SJ and Puntarenas (day trip to the beach?)... as well as buses going north as far as La Fortuna.

Cartago is east of the capital; at a good elevation for cooler living... you will be close to San Jose... but mountains everywhere you look... but lots of traffic.

Bigger towns... more people; probably better 'options' for child care... either in-home, or at a day care center (language barrier...but kids usually don't care!!)

I hope somebody with a little one, or who knows somebody with a little one, can guide you more than this...

Lots of living options... so biggest job is to 'choose'...

Pura Vida

Your list of wants is entirely reasonable, with one possible exception. Especially if your remote work will depend on Internet access, check that very carefully before you commit. Just because the neighbors on either side of the house you seek to rent and across the street have what they consider to be good Internet access, if at all, doesn't mean that it's assured for you.

Depending on the technology that serves your neighborhood, all the available connections may already be committed to others, and the ISP isn't going to expand the system just to accommodate you. Likewise, while your neighbors may have good wireless service doesn't guarantee that your view of a remote tower won't be blocked by trees. As with all utilities, it is essential that you check and re-check availability.