Having lived and travelled to a few different places over time...
Glasgow, UK - Clydeside can be pretty good to take some photographs, particularly down by the Squinty Bridge (or Clyde Arc...). Loads of places down on the coast you can go to take some pictures, but one place that sticks out in my mind is the old disused train yard in Patna! You've also got Arran just a short train/ferry ride away (if travelling from Glasgow Central, book a ticket to Brodick and then your ferry ticket is included as well!)
Edinburgh, UK - Loads of different spots, but Royal Mile and Castle always a good one. I'd avoid staying overnight in the city centre as it can be bloody expensive, but a train across from Glasgow is cheap-ish.
Liverpool, UK - Home town, but Albert Dock and the waterfront is always a winner! If you're there in September/October, then doing sunset at the Tower at the Anglican Cathedral is pretty impressive (can see all the way to Wales on a good day)!
Muscat, Oman - Grand Mosque and Muttrah Souk are pretty good locations. Loads of little fishing villages down near the Muttrah Souk as well as the large fishing market (@kimmy81818 was there recently!). If you like your astro-photography, then a desert trip in to the interior is always good and there are loads of little camp sites and what not out there. If you're a diver and you like doing some underwater stuff, then head out to the Damaniyat islands or Fahal Island, loads of life there! If you're more of a rust bunny, then you have the Al Munassir out in Bandar Khiran. If you do go to Muscat, then rent a car to get about as the Taxi's aren't metered and unless you live there and know the prices you will get ripped off massively.
Musandam, Oman - You can do multiple day dhow tours out of Khasab and the sights at night are pretty damn impressive (no light pollution of any kind). They're more geared up towards divers, so you may get a bit bored if it's a weeklong trip and you don't dive and it can also be quite cold in winter.
Dubai, UAE - Marina District is always good for some light trailing or other night photography. If you fancy doing a trip up the Burj Khalifa, then book it in advance as it is much much cheaper than paying when you turn up! You can also do Creek tours using the water taxi's, it was about 100 AED per person (about 13-15 GBP) when I did it about 5 or 6 years ago, but I had the whole water taxi to myself and we just happily bimbled up and down the creek from Dubai old town. They also have a Souk and a market, but I never really got around to going there (however this will be corrected if I ever move back!).
Salalah, Oman - Try to go down in the Khareef season, but book well in advance as the place does fill up remarkably quickly! If you do go down and you don't live in the region, rent a car as it's easier/cheaper than trying to take Taxi's!
Phuket, Thailand - Loads of different things out and about, but if you're a fan of street photography then Pattaya old street is a good place to go! I went with my family years before I owned a camera, so haven't got any shots sadly.
Vigo, Spain - Cidad de Vigo (?) was pretty impressive from what I remember. I don't remember that much about the place as I rarely went ashore there and the night out we had there was quite a drunken one (to be fair, Spain had just won the 2008 Euro Cup!). I do remember that you can't get food before 2100 in most places and that not a lot of places have menu's and the like in English.
Riga, Latvia - The Riga old city is great! I stayed in a small hotel right in the centre of the old city and then spent the next day happily wandering around exploring the place! I went for the first time in February and was up to knees in snow, so would go in Summer if I was you.
Tallinn, Estonia - Same, the old city is pretty impressive but I didn't have my camera with me that time!
Piraeus, Greece - The port area can be quite interesting with a lot of old architecture and shops and what not.
That's all that really comes to mind for now, I'm sure some more will come along as I think about it a bit more.