If you were willing to fly longer and increase your budget you could look at Mauritius (not much jet lag) and lots of great excursions.
Or increase your budget and try the Caribbean with a Saturday flight .
One of my favourite February holidays (my 50th) was a five start hotel in Prague. I went for five nights so it felt more like a holiday and not a busy city break. I planned each evening to be different, posh restaurant, bistro type place, concert, valentines meal, fun medieval night etc. I also booked lots of lovely things to do in the day including an excursion out of Prague itself on the middle day to a medieval village.
I a did similar holiday in Berlin the following year, basically I threw some money at a city break, stayed in one of the best hotels, with a brilliant location and didn’t skimp on activities and lovely meals out.
I always make sure the hotel has a lovely spa and go each afternoon around 3.30 for a couple of hours before going out for the evening. This way I get to really relax and it gives me a ‘holiday’ feel.
For my 50th on the actual day I went to a concert in a palace inside Prague Castle, looked around the castle and had a mulled wine. Went back to the hotel and had an amazing 90 minute treatment. Walked to an incredible restaurant that had lots of glass and clever lighting which was amazing reflecting on the river. That made a fuss of me there and then I walked back over Charles bridge and it lightly snowed just in time to see the astronomical clock do its thing. Honestly it couldn’t have been a better day.
My friends were surprised when I said I was staying in Europe as I usually go long haul for my birthday but with the right planning it turned out to be the perfect choice.
So it could be worth looking at a shorter luxurious trip rather than trying to make the 1k stretch to somewhere further afield.