or can I see nearly identical things elsewhere?
Probably yes. Anyway, btw of the environs of Belarus, Wilno (Vilnius), the capital of Lithuania, is said to be a very nice once-polish city. There's an unique church of St Anne, which is a late gothic - baroque mixture
http://hiker.com.pl/litwa/img/kosciol_sw_anny.jpg
What exactly is there in Lviv that makes it better than Kiev? Is it just a more historic centre, or something?
Perhaps I'm wrong... but Lwow used to be richer, more colourful... Kiev was a clearly Ruthenian (Ukrainian) city, probably with many jews, but less anyone else, while Lwow was polish-german-armenian-jewish-ukrainian mixture. There are 3 or 4 cathedrals there, for once

(roman-catholic, greek-catholic, armenian-catholic and, probably, orthodox as well)
So south Spain's the way to go? Interesting. Is it truly better in every aspect, or is it more a matter of personal historical interest and taste? Would it be worth going to, say, Sevilla instead of Barcelona, or is Barcelona a must see?
Sevilla is more beautiful, but due to Gaudi Barcelona is more original, I guess.
I've been only to the very north and very south of Spain, so I can't tell if there's much to see in the middle.
Really? I would've thought you'd need 4 or 5 days in Berlin to see everything. Is there not much to see, or does it just not interest you?
Well, what would you like to see there? The historical centre is not that big, and much of the city was destroyed during ww2, so it's not like you have a lot of secessionist buildings to admire.
Oh, btw of this region, you can save yourself the trouble to visit Sanssouci, it's nothing special.
Dresden is said to be a very nice city, though - but I haven't seen it, so I can't tell.
Would I be correct in assuming I could see pretty everything interesting in Brussels in one day?
Most cities you can visit in 1-2 days, if you start early. But it always depends if you want to visit museums and how many of them, if you want to go dancing or something, or not. If you want to go to a restaurant to taste local food, or not. If you want to take brakes during sight-seeing, or not. I don't know you, I can't tell. I do recall correctly there was much walking in Brussels, more than usual.
This is particularly something I'm not sure about. Barcelona or Bilbao? My sister went to both, and she says that Barcelona wasn't that great, but that Bilbao was brilliant. Is Barcelona just sand and beaches, or is there more to it that I wouldn't get from, say, Bilbao?
Haven't been in Bilbao, unfortunatelly, so I can't compare.
When it comes to Athens... It depends. If you're a fan of ancient greek history, it's worthwhile. If you haven't seen too many ancient ruins yet, it's worthwhile. Go there, otherwise once you may regret that you haven't gone there.
Siena is lovely. there's the cathedral
http://www.travel-destination-pictures.com/data/media/27/siena-dome-interior-italy_744.jpg
the main square is beautiful
http://www.casasisti.com/gallery/itiner/siena.jpg
and there are some nice paintings in the town hall, if I recall
The entire old city has a similar, warm colour...
Well, I don't know. I just recall it as one of the nicest places I've been to.
Anyway, if you come to Warsaw, I can show you around the city I guess.