How old are the DC?
DH is a teacher so we do school holiday times only.
For much less than your budget in school hols we've done 4 nights 4* New York two luxury rooms all meals, transfers and spending money.
11 days around Italy. 1st class trains staying in Florrence in a nice big apartment for a few nights including train down to Rome, then train back upto Venice and we stayed out at Lido de Jeslo but got the ferry across to Venice. In Florence we had breakfast in the apartment (fresh pastries every day), we tended to have street type snacks from the covered market for one meal and restaurant another. In lido we stayed in a three bed mobile home on the beach and cooked more (I love cooking though) that break was under £1500 all expenses, travel, food for the five of us.
Luxury rental in Croatia with flights. Five beds, three bathrooms, multiple terraces, swimming pool, small football pitch around £600 for a week. Easy jet flights were £300 and car hire was £15/ day. We self catered and drank lots of local wine. Again an Easter break.
Last summer we went Eurostar to Paris and had four nights in a nice hotel. That was about £1000 so quite a bit for us.
Hamburg just after Christmas was only a few hundred in a central hotel with flights. Berlin at Easter was similar. Vienna at Christmas in an apartment for a few nights similar too.
Chamonix was another lovely one. Flights and acomodation under £500 for 5 nights. We did spend a fair bit £200ish on 3 day lift passes to go up the mountain, on the mountain train etc. Well worth it though.
Prague for a week, massive apartment right on the Danube by the famous bridge, name escapes me, so great for restaurants and fresh baked goods for breakfast. Acommodation and flights were about £1000/ week night of summer but eating out, travel and entrances were really cheap.
If you're near a town and don't need holiday clubs, I find apartments/ houses much nicer than all being hauled up in a hotel room. I cant get my head around the price difference. In Chamonix a 3 bed appartment was £200 for the 5 nights (autumn half term very end of summer season) 1 room in a hotel for the 5 of us was £200/ night. I do budget for the food. Breakfasts the DC loved coming along to buy baguettes, hot croissants and lots of meats. I liked having a big pot of coffee on the go and a fridge to keep some wine for when the DC retreated to their own space. Being well located means lots of restaurant food choices.
We've been to Iceland summer and winter and Denmark. Again luxury accommodation and semi catering. Both amazing countries.
Another option that would fall well within your budget is a cruise. Southampton to Southampton gives you various options. We've done the P and O mini breaks taking in bruges and Guernsey and a week cruise to the Norweigen Fjords (worth paying for a balcony to enjoy the views on that one)
This Easter were back to Italy flying to Naples as we missed Pompeii off our tour and regret it.
When we were in Hamburg I picked up a leaflet on a safari park near by that had sleeping lodges and safari tents in amongst the animals. It was very affordable and is on my list as a future tour possibility flying into Hamburg (the DC loved miniature wonderland) couple of hotel nights Hamburg, few nights safari lodge, few nights in a thermal spa somewhere then fly back from wherever is nearby. DS1 loves train travel so we'd hop around by train between locations.
If you say a little more about ages and interests I'd be up for throwing a few more of our destination details into the mix.