Where to stay – 2 young families in April – pls help?

We are coming to lisbon mid April and looking for any advice on where to locate ourselves for our stay. We are travelling with 4 adults and 4 children (ages 4 and two infants). Our total time is 2.5 weeks and we would like to stay in or near lisbon for part of the trip but not sure what neighbourhood. We would definitely like to be very close to an area with shops and restaurants as we will be making trips to and from the apt often for naps etc. Would it be best to stay right in the city centre? Or is there an area with lots to keep us busy that we can easily travel into lisbon.... Also looking for suggestions on other nearby towns we can visit for a few days. We only want to change locations a maximum of 3-4 times as we will be slow with all the kids in tow. We are looking at staying in apartments or rentals all together (no hotels). Any advice would be greatly appreciated