So once you get into grad schools and make your decision April 15th, you suddenly realize you still somehow have until September before classes start in the fall. I found myself around that time wondering what to do with that summer in between. What I ended up doing was working as a summer researcher here at UC Davis; but that's boring. Let me say firstly why i ended up doing that, and secondly how I ended up doing that, and how it worked out.
At first glance, it seems absolutely obvious that what you should be wanting to do is research with a potential adviser, since (a) it pays you money, and (b) it's what you applied to grad school to do, isn't it? But truthfully, I didn't find it so simple. When thinking about what I wanted to do that summer, I came up with 4 options:
Let me start with the caveat that when I applied to grad schools, I was 2 years removed from undergrad, and 2 years further removed from most of my undergraduate physics courses. As a result, I was kind of fuzzy on most of my physics. Also, I was working, so I had some money saved. Part of me wanted a last hurrah; I had no commitments for maybe the last time until retirement, so taking a year off sounded pretty awesome. And because of my general haziness on physics, I really felt like a good use of my time would be to work through my undergrad books again (and maybe some grad texts) to keep myself sharp before the start of school. And research, of course; I had worked in the field for several summers, and had a publication, so I knew I liked it. I also knew spending time doing research should at least theoretically move me forward in my degree. In the end, I kind of fell into my decision; a professor with some extra money mentioned he'd like me to start early, and I couldn't find the words or will to refuse.
How did it turn out? As far as research goes, pretty disastrously. I got hardly anything finished, and my rustiness was evident. Worse, that and finding a place to live took up all of my free time, so I had no time to study; I was in a near panic mode when orientation week rolled around, a diagnostic test was handed out, and I couldn't even remember how to find an eigenvector. But it did get me two things. (1), it settled me in earlier, I met students in the department, and made friends more easily. And (2), the time I spent doing the research (which mostly was reading papers) made seminars more intelligible during the school year--I really learned a lot of cosmology. It also (somehow, despite my general uselessness) got me a group; I was invited my first year to work as a graduate student researcher (a rarity at least here at Davis), and am working towards the first set of publishable results this spring (putting me further ahead than my first year peers research-wise).
It did cause me to miss out on some things, though. Firstly, it means I won't get the vacation I wanted to take, which might backfire year 4 of my PhD when I'm totally sick of northern California. Secondly, by not studying, I was totally unprepared to attempt the preliminary exams the first week of grad school (again the eigenvector thing). If you take the preliminary (which is on advanced undergrad/simple grad physics) and do well, it gets you out of first year courses. A few of my friends managed to do that; they have way more free time during the school year (which means more fun AND more research), as well as putting them ahead in their coursework in their particular discipline. Not passing that was a missed opportunity I might have seized if I devoted part of the summer to studying.
Practically, if you do decide you want to try to do summer research in between undergraduate graduation and graduate enrollment, make sure you use your campus visits to query professors about available projects for you during the summer. Don't be afraid to bring up the issue of money; if you're coming in early, a GSR is your only possible source of support. And don't worry if you can't get the professor you really want to work with right away, the main advantage is the time spent learning the subdiscipline--a summer of research doesn't commit you to a professor.