I got a Bee+ and Maxi Cosi car seat for getting taxi's and getting into relatives cars.
The Bee has been an absolutely amazing pushchair and I picked it because it could do everything including have a reverse seat position. My friend had a Maclaren with all the bells and whistles and even though it is also a great option, the Bee's lighter weight and smoother handling made it a dream for getting trains and buses.
After a year, my DD has become heavy enough that I felt I needed an even lighter and more compact pushchair. I recently bought a Maclaren Triumph and use both of my pushchairs daily depending on what I am doing. The triumph is for days I know I will be getting public transport and the Bee is for weekends and days I don't leave my local area.
Also, invest in a really good baby carrier. I bought a Beco Gemini and I take it with me everywhere.
With the Bee, I never folded it to get on a bus as the fold is too bulky. I would rather wait for an emptier bus, but that's a choice I made. I would pick the Bee up with DD inside for going up and down stairs, that's why I needed something even lighter now DD is older and heavier. But, I don't pick up my pushchair if I can help it and use a combination of baby carrier and Maclaren now for busy days out on public transport or when I know I will be going up and down stairs. The triumph is so light and has a 10 second fold (once you get used to it) so great for buses.
In my experience, living in the city means needing a few different options for day to day travel. I think one pushchair like the Bee to begin with and then a lighter option like the Maclaren Triumph when baby is old enough to sit in a partially reclined seat. Plus a baby carrier to use in combination or by itself for quick trips out.
I wouldn't recommend a baby carrier for all day wear as it can put a lot of pressure on your back once your baby gets older and heavier.
Don't get an expensive car seat if you don't need one. I only got the Maxi Cosi because I thought I would be going on trips in my DM's car more often than I actually did. I only used it about a handful of times so it was a waste of money. If you do use cars, taxi's or other, regularly then I would get a compatible car seat.
The Bee is expensive and I think there are cheaper options on the market now. I bought mine as an investment as I plan on having another baby. That's my other tip, make sure to get things with a reputation for lasting long when you have to put them through the battering of city life. For me, this meant spending more. Everything I bought was expensive IMO, but will last me long enough to use again.
HTH 