Lisbon is known as the "City of the Seven hills". That means its kind of up and down a lot of the time. The most flat areas are near the river.
I'm born and raised in Lisbon and it was until I went around with my own children that I realised some possible problems that are worth sharing here. To compensate for these "down sides" I should say also that Portuguese are in general very welcoming people and love children. A big plus is also the fact that everyone will happily go out of their daily routine to help out if you need some help with lifting the stroller and they will also happily share their seat in the train/bus for the comfort of tired parents.
If you are visiting with strollers you should also think about the pavement (sidewalk) being often quite narrow, and Portuguese drivers parking quite often using part of the sidewalk.
Another annoying issue is that many road signs (signs for drivers) are placed in the middle of the sidewalk, which being narrow already, often forces strollers to go on-and-off of the road to get around them...
There is a website that has nice information for traveling with Children, from a mother's perspective. Apart from the renting options it has really nice information about children in Lisbon and in each house.
If you rent inside the city, your distances are of course smaller. I would say rent near a subway station, and somewhere with an elevator. You might want to stay near the coast, in a suburb like Oeiras, where you can get into the city center in about 20min and still be near the sea for beach and bathing.
I must add, as you can read in nsn's nice answer that I don't agree Lisbon is 90% flat. And what I mean with that is that is that most of the nice tourist attractions, traditional neighborhoods and some of the finest restaurants are in the older parts of the city which are hills.
There are also flat areas, yes. As I mentioned above, near the river you find wonderful places, easy to walk and spend some nice time. One of these areas, and a must for Children is the Oceanarium, it's really worth it. Another must is the ZOO and definarium which basically are in the same "park".
One last recommendation if you are into visiting during June-August season, Lisbon gets warm. Think about extra drinking water and maybe an ice cream here and there :) For our six year old daughter this is not a luxury, she doesn't walk if she is too warm.