While a course on problem solving could prove helpful, I believe that the environment, the peer group is more important. The authors of CP Book teach at NUS, most good universities provide courses on DS/Algo, I'm not sure whether you're referring to Competitive Programming — Problem Solving or otherwise, I'll assume it's Competitive Programming. To find good unis with strong competitive programming culture, just check organisations in your country, or even internationally — if you're fine with that.

Disclaimer: This is from my personal experience and doesn't necessarily apply directly to you.

I've realized that in the US, many college computer science programs/majors don't revolve around heavy problem solving. The college CS classes I've taken so far spend more time memorizing some new syntax and applying it to standard problems that aren't fresh. In other words, CS to me feels like a waste of time since the stuff I was doing didn't feel fulfilling nor did it stimulate my mind. This is why I've switched to a math major recently (still minoring in CS) and since then I've gotten my fair share of thinking and problem solving that I enjoy.

Of course, this doesn't mean you will not enjoy college CS courses, but I just wanted to post my opinion when you mentioned you looked forward to "problem solving-related courses." Hope this helps! :D