It's the library where I first took part in a summer reading challenge. The more books you read, the more write-ups and pictures you got of certain dinosaurs, and hey, dinosaurs! Cool!
That library's since moved, but most libraries I've known are still around and where they were when I went to them. Including the very first one I remember, the school library at Westwood Elementary in Rancho Bernardo, CA, where I lived from 1976 to 1981. IT WAS ROUND. It was in the middle of campus, with classrooms encircling it.

The main detail I remember from there was a row of portraits of U.S. Presidents, first ending with President Carter and then (for my last few months in town) President Reagan. It's where I first read Shel Silverstein. Probably also where I first attended a Scholastic Book Fair, come to think of it.
Being Navy, we kept moving. Virginia Beach next, first a rental house on Lord Dunmore Dr. then a home Mom and Dad bought on Little Lake Rd. Both houses weren't too far from Virginia Beach public libraries, either, and since Virginia Beach by necessity sprawls, that was a bonus. (It's built around a bunch of bays, lakes, streams, swamps and Oceana Naval Air Base. It had to adapt.) I sort of remember the Kempsville library, I definitely remember the Great Neck library.
Vienna, VA had the extra bonus of the town branch being really easy for me to reach on bike, about a block from the W&OD Bike Trail, which is near the house I lived in from 1984 to 1987 (and where I started seriously bicycling). I was at the Patrick Henry branch a lot, through high school (which was also in Vienna). I read several of L. Frank Baum's Oz books there, circa fifth and sixth grade. Fairfax County has a decent public library system; I took advantage of that, plus until I started driving in 1990 my folks had no problem dropping me off at a lot of branches.
Then I WORKED IN A LIBRARY. My first non-temp job, for about a year at college, was at the IMC, the Instructional Media Center in the Knight Library's basement (and not to be confused with the International Machine Consortium from the film version of Contact). I'd roll TV/VCR carts to classrooms, and I also was a projectionist. I got to show 16mm copies of The Godfather — five reels, not the usual three for 16mm copies of feature films — and others in either an IMC screening room or PLC's big auditorium. I still feel bad about when I got a print of the Polish film Korczak that had its reels divided up differently than a previous print I'd used, so Reel 1 ended before I'd expected it to end. YES, I WAS THAT PROJECTIONIST (once, just once, I hope).
It's ingrained enough into me that I didn't realize it for ages, but the farther from a library I am, the slightly more "off" I feel. It helped when I lived in the small (for me) town of Hermiston, OR to have the town library be two blocks away from my office; not long after my parents moved to Dundee, OR, I tried walking to the Newberg library nearby, and that's at times a harrowing walk but I wanted to be sure I could do it; my first place in Portland was within walking distance of Multnomah County Public Library's Belmont branch; then I lived in an apartment that was...that was a 45-minute walk from the nearest branch (in Sellwood). Which I'd still do sometimes, but I felt the (somewhat) greater distance. My current place? Within an easy walk of TWO branches, and a short bus ride away from others. Score!
Also, after all this, you won't be surprised that getting my Multnomah County library card was one of the first things I did once I'd moved to Portland in 2001. Oh, yeah. Still have the same card.
Read well. Libraries want and like you to.