I would second Japan, a really great choice. Also, as @greenskylark said, combining that with South Korea could be an interesting choice. There's a thread here about somebody currently planning a holiday in Japan.
https://www.mumsnet.com/talk/holidays/5152514-japan-planning-thread
For where I live, Easter holiday dates are Saturday 5th April to Sunday 20th April.
Within those dates, flights from London to Tokyo leaving on Monday 7th and returning Friday 18th are less than £1,000 with China Eastern (stopover in Shanghai).
If you want to travel at the weekend it will generally be quite a bit more expensive. But there are still some weekend flights for less than £1,000 but they involve two stopovers (London > Beijing > Osaka > Tokyo) with Japan Airlines and Air China.
For example, depart London Saturday 5th, return Saturday 19th, £967. Or you could just
.
Or China itself has lots of different areas to see and things to do. Flights to Shanghai then start at £600 and flights to Chengdu start at £680
.
Another alternative would be India; Easter is a great time of the year to visit. I would look at northern India, flying in to Delhi or Calcutta. If you're in that part of India then you can also cross into Nepal and visit Kathmandu as well (well worth doing).
During Easter, weekend flights to Delhi from London start from £750 for direct flights (eg Air India) or £540 with one stop (eg Swiss, Lufthansa, Finnair etc).
Flights to Calcutta start at £620.
Then with all these destinations, you can spend as much or as little as you want on the standard of your accommodation and how else you spend your money. Five star hotels are going to be more expensive anywhere that you go compared to more modest hotels.