What are some good ways to finish the body of a letter (see details)?

“I just thought I’d let you know what I’ve been up to you since I saw you last. I hope all is well with you and your family!”

Or something like that.

“I hope you enjoyed reading about my adventure as much as I enjoyed experiencing it.”

or

“It’s nice to be able to share the experience with you.”

As to the closing—yes, “sincerely” seems a little formal—maybe “with regards” or “hope all is well.”

and if this is a school assignment, I’m in trouble with Jeruba now ;-)

Not a school assignment. It is a personal letter to a former teacher (not a current one).

I guess I’d include a little note (if you haven’t already) about why you decided to write to a former teacher instead of, say, a lover, close friend, or relative. What made you direct the letter this way instead of some other?

@WasCy It’s a personal letter. One of the people I am writing to is a former teacher.

There’s nothing wrong with what you’ve written. I’d worry about it only if I were going to be graded on it against a prescribed form or guideline.

But you might conclude by asking after the teacher: How are you? How have you been? Are things well with you?

@weeveeship I understand that it’s a personal letter to a former teacher. That was clear. But why a former teacher instead of a former employer, mailman, doctor, or grocery store clerk?

Do you see my point? Teachers (anyone, I suppose) enjoy hearing from people that they’ve helped along the way, in this case a former student. But there’s context to consider. Do you have a shrine to this teacher in your bedroom closet and chant her name every day? Or did something occur that reminded you of her, and that’s why you’re sharing the story? Teachers like context. Instead of leaving her puzzling over, “I wonder why he wrote to me after all these years?” I’m sure she’d be thrilled to hear that something in your trip reminded you, perhaps, of something she once said in class, and that led to other memories… all of which resulted in the letter. She’d love to hear about that. She won’t want to hear about a shrine in your bedroom closet.

@WasCy Oh, I see. Yeah, something in my trip reminded me of something she once said in class (it was a science class). So, I think I’ll include that in my letter.

There you go. She’ll love to hear about it.

I would thank him/her for having an influence on you, and that, as an adult, you really appreciate the extra effort they put in with you/the class/the subject. Sign it “warmest regards.”