Hi, we are excited to take our 13 month old to these two wonderful cities in Portugal later this month. I'm just wondering if there's anyone out there with experience of taking young ones there? Would you recommend taking a stroller everywhere or simply put the baby in a backpack carrier? I've heard that both cities are very hilly so I'm not sure if there are also a lot of stairs that I'll need to climb. Thanks in advance.
make sure you use one of these. http://store.ergobaby.com/
not a babybjorn or similar. We never brought a stroller on trips.. too cumbersome for the reasons you mentioned.

jjjoejr,
It depends on what you want to do in Lisbon.
As always, tourists tend to have a partial view of Lisbon. Lisbon is both hilly and completely flat.
Understand that Lisbon has more than 20km of riverfront's straight line. IF you want to be only on the riverfront, there are no stairs to climb. You will be always at sea level. Of course not all riverfront is for visitors or residents (because of the port, docks, etc) but if you want you could spend the entire day playing with your baby in the gardens looking to the river. You can do that in Belém, Parque das Nações and nearby the downtown.
All Lisbon's downtown and the proper center are flat. The only hilly regions are those that stands between the river and the proper center. In some areas it gets too steep, but of course you could take buses or trams and even the subway\metro to some areas.
Now if you want to walk all the time, and visit the hilly parts, the backpack is the better option.

What MNESLCL wrote about Lisbon is also true for Porto. The city is situated along the river Douro and the part directly along the river is flat, but just away from that zone you have to climb to the center. I always find it rather steep, but am much older than you. In the center itself are some rather flat parts.

Lisbon is not only hilly but there are many streets with pavements too narrow for a stroller. As mentioned by #2, there are many flat parts of the city but the hilly & narrow ones tend to be the most picturesque. If you want to have more freedom to explore this fascinating city, take a backpack.

Thanks everyone. One more question regarding the baby-friendliness of Porto and Lisbon. How likely are you to find a high chair in cafes and restaurants? Thanks!

Thanks everyone. One more question regarding the baby-friendliness of Porto and Lisbon. How likely are you to find a high chair in cafes and restaurants? Thanks!
Well, i believe none in regular restaurants, i guess. Though i must tell you that in Lisbon there are several restaurants with an exclusive area for children, so you might find there. I think that most of shopping centers have an exclusive area for babies too.
Couple of restaurant's examples:
http://www.canela.pt/os-nossos-espacos/espaco-canelinha/fotografia.html
http://www.noobaicafe.com/ (check the gallery on this one, the big frog lol).
http://www.grupodocadesanto.com/en/doca-de-santo/galleries/Doca-de-Santo/50/