Of course you want to come to Brooklyn. If you want to stay Downtown (Brooklyn Heights, Cobble and Boerum Hill) or further towards the park (Gowanus, Park Slope, Prospect Heights), these are some options that I know of. If you know any other decent options, please let me know!
Generally speaking, hotel options don't seem great, surprisingly. They're either in really weird places or are far from where you want to be, especially if you want to be further away from downtown Brooklyn. There are a few decent ones I list below.
On Smith Street in Cobble Hill, which is full of restaurants and Bklyn shops. Modern furnishings, and bright looking rooms. Cool looking options, including quirky rooms with bunk beads or hammock. I lived in this neighborhood from about 93-98 and love the hood. Funny to me that there's a jail across the street, but you won't even notice it there. Not very convenient to our house, about 1/2 hour walk to Park Slope. Near F train and a 5 minute walk to 2, 3, 4, 5, N, R trains.
Downtown big hotel experience sandwiched between beautiful Brooklyn Heights, downtown court houses and NYU Polytech area. Short walk to Brooklyn Heights or Dumbo. Nowhere near my house. We've stayed here when we've had to be out of our apartment, and it's the chain experience you'd expect. Near 2, 3, 4, 5, N, R trains.
THE best option if comfortable staying in someone's place I think is to search Airbnb. Among the options I've found some beautiful homes that really put your more into the neighborhoods that you want to be in than the hotels can. Check the ratings and comments.
I haven't yet had people stay in these particular B and B's but these are the ones we've looked at that are near our home and the park.
The Park Slope Bed and Breakfast
This looks like the ideal brownstone experience. Owner Josie gets great reviews on the sites below, and it's in a great location in center Slope and a block from the park. 3 flights of stairs, so be fit if you want to stay here. I live in a 4 story walkup, so I know that lugging luggage is rough, but my advice is to just pack light and you'll be fine. About 5-10 minute walk to 2, 3, F, B and Q trains.
At Home In Brooklyn
I haven't had people stay here, but it gets good reviews and looks like it's the brownstone experiene you may be looking for, even though it's not technically a brownstone. Around the corner about 5 blocks from our house, and right across from Prospect Park. This is a few blocks from the arch and the Saturday farmer's market and an ideal location for getting to restaurants, Brooklyn Botanic Garden, the Museum, and trains. Near 2, 3, B and Q trains.
See also the reviews in the Google listing.
3B, The Downtown Brooklyn Bed and Breakfast
Located downtown on Lawrence between Jay and Bridge Streets in the Metrotech Center area, near NYU Poly and Fulton St. It's a A short walk to Brooklyn Heights, and a longer walk to Cobble/Boerum Hill and Fort Greene. The immediate area is primarily commercial with some residential spots and new rehabbed buildings gone residential. 3B place looks like a co-op living space managed by a Brooklyn creatives that run a little BnB with private rooms and a communal bunk room on a 3rd floor walk up with high ceilings. Breakfast included.