I'm back from Berlin and just wanted to thank all the forum members who responded to my questions prior to my visit - you were a great help!
A few thoughts/experiences:
Safety: I travelled alone, and while I did spend some of my time getting a little lost on the U-Bahn/S-Bahn, at no point did I feel unsafe or nervous. Kreuzberg was probably the only area where I may have felt slightly uneasy at times, but it still felt safer than Dublin.
Food: if you like ice cream, visit Vanille & Merille, in Kreuzberg. Some of the nicest ice cream I've ever tasted (try the cherry - lordy, it's good!). If frozen yoghurt is more your thing, Yoli on Invalidenstrasse is excellent (the yoghurt isn't at all sour…unfortunately the staff were). I ate at Mao Thai on Woerther Strasse, in Prenzlauer Berg - delicious food and good service. I also sampled the Currywurst at Curry 36 in Kreuzberg (a minute from Mehringdam U-Bahn) - be prepared to queue with lots of hungry Berliners! It was very tasty, though I thought that the sausage perhaps wasn't as amazing as I've had elsewhere. I recommend buying bread rolls and your morning bretzel from small bakeries - they're so fresh and delicious (the sunflower seed broetchen was my favorite). For a treat, buy a cake or bun from Lindner Feinbaeckerei - there are several branches around the city. I didn't visit many bars while I was in Berlin due to being alone, but I did pop into Prater Garten on Kastanienalle (Prenzlauer Berg), and enjoyed a beer and some people-watching under the chestnut trees.
Museums: I only made it to two in the end. Neues Museum was very impressive, and beautifully curated. The building itself is striking too. Nefertiti, understandably, has a room to herself. I pre-booked my ticket online for 10am, and sailed straight in with no hassle at all. I also visited the Broehan Museum, in Charlottenberg. This museum is dedicated to Art Deco/Art Nouveau. It's laid out very nicely and while I wasn't so impressed with the paintings on show, the pottery and glassware, furniture and other pieces were beautiful. There are some lovely items by Hector Guimard, the chap who designed the famous Paris Metro signs, and a fascinating video of German glassblowers at work.
One of the highlights for me was a visit to the flea market in Mauerpark on Sunday afternoon. I wasn't prepared for how big it was! People were selling pretty much everything you could think of, and there was a great buzz about the place. Buy yourself a beer and some corn-on-the-cob, and take a stroll around the stalls. There was karaoke going on as well, which drew a massive crowd.
I also recommend taking a stroll through Tiergarten - I found myself a bench in a shady area and fed the birds. I was only a few minutes' walk from Potsdamer Platz but it felt like I could have been in the middle of a forest, it was so peaceful.
Travelling: I bought day passes (Tageskarte) while I was there and relied on the U-Bahn and S-Bahn to get me about. Very efficient and reasonably-priced transport. If flying home from Schoenefeld Airport, I'd recommend catching the Airport Express train from Alexanderplatz (if practical) rather than from Hauptbahnhof - I found the latter confusing and a little stressful due to its size. If you're a little nervous about crowds, Alexanderplatz is more manageable.
Ich liebe Berlin! :)