You arrive in Lisbon on Feb. 10. If that's from the US or Canada, the overnight flight is likely to leave you sleep-deprived and jetlagged. I, personally, don't count my arrival day as a real sightseeing opportunity. It's more a day to walk around outdoors and try hard (not always successfully) to stay awake until after dinner. You need to travel to Barcelona no later than Feb. 16, so that gives you only five full days in Lisbon. You can easily fill that time with the city itself and Sintra. If you want some time in small towns (don't know whether they will be dead in February), you can try Obidos or perhaps a bus tour that takes you to several places. If none of those options appeal, you can head to Barcelona a day early.
If you arrive in Barcelona on Feb 16 and leave on Feb 22, you have only five full days in Barcelona. That is not a long time for that sight-rich city. I definitely would not plan to take 3 day-trips if I had only 5 days and a few hours in Barcelona. It's very time-consuming to change hotels, so I would not choose to do so in order to spend one night somewhere else. My first choice for a day-trip from Barcelona would be Girona rather than any of the places you mention, but of course that decision depends on what sort of things your are interested in doing.
If I had your fixed parameters (the flights), I'd probably opt to spend the first five nights in Lisbon, travel to Barcelona on Feb 15, and either spend all the remaining nights in Barcelona or spend 2 in Girona and the rest in Barcelona. Figueres is a shorter day-trip from Girona than from Barcelona, but I'd only change hotels if I valued the opportunity to spend two nights in a charming smaller city that is a lot less hectic than Barcelona.
However, before deciding on how many nights you want to spend in Barcelona, you need to spend some time with a guide book to the city so you know what sights you want to visit. Barcelona has many that require prepurchased, timed tickets, so if you have an interest in those sights, you really cannot wing it and will have to lay out a partially-fixed itinerary. You cannot simply start out each day with vague plans and cram in as much as possible, which makes Barcelona not the place for a hit-and-run visit if you are the typical tourist. You also have the soccer game to attend.