I have been on several mission trips (mostly secular) and agree with the notion that it is extremely important to examine your motives. I understand that you're not interested in a 'missional vacation,' and that's a good start. Wanting to give back is a far better reason to want to go on mission trips. The first trip I went on was one to Haiti when I was 18, and while I went wanting to help I'm not sure I did any good at all. I learned a lot and my perspective on a lot of things changed drastically, but in retrospect I was more of a burden to the people around me than a help. I didn't do anything stupid like get drunk and act like a fool, or crash any motor vehicles, but I didn't contribute anything useful to the people around me, either. So I've tried to do better and be better since then.
Partnering with 'boots on the ground' so to speak is a far better idea than a group that goes down from outside once or twice a year and expects the host country to do things the way the outsiders want. People who live and work in an area are going to have a far better idea of people's actual needs and what interventions will actually work.
I would also highly recommend reading the book 'Toxic Charity' by Robert Lupton
before embarking on any sort of mission trip. I didn't read before I went, but wish I had.
Finally, wherever you do end up going, it's important to know where you're going. It's good to know culture, yes, but history is also important. Is the place a former colony whose people and/or resources were exploited by the colonizers? There might be some (understandable) resentment/resistance toward foreigners coming in ostensibly to help. Recent wars or conflicts? Were there outside governments meddling? (ex. USA/USSR in Afghanistan and Nicaragua) Realize that you might not be welcomed with open arms. (*alternately, you might be humbled by people's kindness to you despite the sins of your government. That works both ways.*)
I don't mean to sound like I'm discouraging you from going. I'm not. There are wonderful people doing wonderful work all around the world, and expanding our own horizons almost always makes us better people. I just think it's v important to go for the right reasons, to respect the dignity of the people you're going to be serving, and be a responsible steward of the privilege you're given as a guest in someone else's country.