Google maps is great for getting current hours (travel guides aren't as current). Short story long:
Start at the Library and check out travel guides for the places you want to go. Decide which sights seem interesting to you (based on your own personal interests). Check out tripadvisor.com's list of things to do in cities (to make sure you didn't miss something you might like). Buy, and take, the travel guide that you like most (I prefer taking a Kindle version for my smartphone).
That gives you a list of things to do. I generally plan one thing in the morning, lunch, then another sight in the afternoon. I can do more but this keeps me from pushing too hard on my vacations. That decides my number of days in a place. I also keep a list of other sights that are a notch below my must sees, things I'll do if I have time. I'll add something whenever I'm up for it and have time.
Once you've done all that, sit down with Google maps on your computer. Click on each of your must sees on the map (or search using the panel on the left). Most sights will show the current hours for the sight. These get somewhat longer as you approach summer then get shorter after summer. Right now is about the shortest hours so check back a little before your trip. For example, if you want to visit the National Technical Museum in Prague, click on it in Google maps, look down on the left panel where it says something like: "open now, closes soon, closed now". There's a scroll down next to that with current hours, click on it. The technical museum is open 9-6, six days a week and closed Mondays.
Monday is a common closing day for European museums, but it's not something to rely on. I wanted to see a museum in Beaune, France. I arrived in town early Monday afternoon but went early on Tuesday only to find out that museum is closed on Tuesday.