If you’re looking for a decent cafe, space, or place to work in Prospect Heights away from your tiny kitchen table, you need to venture outside. But perhaps the biggest problem is avoiding loud music, baby/toddler, bustling lines of customers, and other distractions.
One of your first stops should be the Central branch of the Brooklyn Public Library, which is open late and has wifi. Some find the main branch library at Grand Army Plaza to be too noisy; if that’s you, check out these other Brooklyn Library locations. The smaller neighborhood branches tend to be 1-2 rooms, but are pretty quiet as long as you aren’t there during “story time.” Try the branch at Franklin Ave, just off Fulton Street, or the Crown Heights library (St Marks and Nostrand).
Prospect Heights bars such as Sepia tend to be open but relatively deserted during the day. At Soda Bar during the day, ask the bartender (nicely) to turn down the music, and they usually will.
Coffee shops are usually favored by laptop campers, but in Prospect Heights, you should probably avoid Joyce, Sit and Wonder, Milk, and all the other coffee places: they tend crowded and noisy, with no outlets, lots of babies, and reportedly, customers who won’t share a table. The Glass Shop in Crown Heights is hip, but baristas play music loud enough to eradicate productivity from the most disciplined brain.
Dean Street at Dean and Underhill opens as early as 8 am. Scones, muffins, coffee, nice atmosphere and pleasant staff. I don’t remember that there’s any music.
And if you don’t mind a bit of a trip, check out Study Hall at Proteus Gowanus, a “place for quiet contemplation, study, and work” open every weekday (Monday through Friday) from 10 a.m. to 6 p.m. If quiet work space with WiFi was not enough, they also have fresh coffee, occasional snacks, and small cubbies you can use for supplies and notebooks. They want $50 for a month’s membership, but think of all the “guilt purchases” you’ll avoid by not working at a coffee shop or bar, where you could easily spend $20 per work session to keep the barista/bartender from shooting you surly looks.