Favorite: courses not overly long where there are holes that offer different ways to play some of the par 4s and 5s, not just mindlessly picking up driver all the time. I really enjoy the challenge of Pete Dye courses.
Least: courses with an over abundance of water and forced carries.
I’m taking a more literal interpretation of your question. My favorites were Augusta National and Cypress Point. Both courses were designed by Alister Mackenzie. Genius. Least favorite was Kiawah Island Ocean Course....if you miss the fairway, you’re screwed.
Critical elements to me (didnt take this as a specific course but could share that if this develops..
Favorite- Greens are the key to a great course, I have rarely seen a "great" course that did not have excellent greens...conversely, I have rarely seen a course that didnt have great greens also have great care for the tee boxes, and the fairways. Clearly, all courses have unique elements....for instance, a large part of Ocean courses have blown out areas due to sand, wind, and heat, but it does not take away from the overall vantage point of being on the ocean...Similarly a mountain course usually has an issue with winter issues, but then provides some of the most spectacular views...
Least Favorite- I generally am sad to see great courses, or once great courses, that have just let themselves slip to not caring about what matters...and again, for me the lead indicator is always the greens...then it shows on the tee boxes, and then fairways, bunkers. etc. So I would say my least favorite is a course that has the chops, but not the commitment to being what it could be...I can enjoy a straightforward wide open easy course, so that is not the issue at all, it is all about expectation...I hate going to a Nicklaus/Fazio/Faldo/RTJ, etc. course and see it just in disarray...
I tend to agree that really good greens can make up for a lot of less appealing traits, also really high unplayable rough makes a Course much longer and not fun.
We see the lush rough a lot where we play and sure you are not suppose to to there but reality is we will find more rough more often than otherwise. If I could pick a favorite type it would be mountain or more hilly Courses as apposed to the flat typical Florida layout, but that maybe just do to flat course burn out.
My answer is the same for both questions, and specifically my home course.
It is my favorite because it is challenging, scenic, close and relatively inexpensive.
It is my least favorite because it can be so punitive, especially with mishits. You really need to know the course to know where you should put the ball on any given shot. In the middle of the fairway is wrong for most holes. If you mishit you are cooked on a lot of holes. It really pushes you to be accurate.