First of all, I suggest that you'll have a look at a very similar
question (regarding Fabruary) that I've answered several years ago:
Holiday in February
My suggestions on this answer still stand: Israel, Jordan, Egypt or
North Africa would all have wonderful weather by March (in comparison
to Germany...) and will be also very special for a holiday. Especially
Israel (if you integrate the holy sites) or Egypt (pyramids, etc.).
Both of these have luxury hotels. The UAE is unfortunately also out of
the question with your budget, but very good hotels+flights in Israel
or Egypt could be found for 2000-2500 EUR.
Another option for this budget could be to book (as soon as possible)
a budget flight from Hamburg to the destinations offered by budget
flight companies, which includes Southern Spain, Southern Italy and
Hapag-Fly - Plan for Winter 2006/07 (you should look under HAM):
- as you can see, the company offers weekly flights to Tel Aviv, Elat,
Cairo, Luxor and Sharm-a-Sheikh.
Cheap Flights from Hamburg
And from Luebeck
In Italy, weather is a bit trickier this time of the year (rain might
be expected), but is certainly - in Southern Italy - warmer as it is
in Germany; so Sicily or Basilicata is recommended destination. The
latter is still very undevelped. Up to the north, Capri is very
romantic (and expensive) and Florence offer culture.
Israel Travel Tips
I hope this answers your question. Please contact me if you need any
clarification on this answer before you rate it.