Budapest?
Not in February. It's cold, dank and grey most of the time.
Seville is great. Depending on how long your break is, Jerez, Cordoba, Granada (the Alhambra used to be free on a Sunday - might still be) & Cadiz are a train ride away - although check out the buses, as they are cheaper, more regular and almost as quick (well, they were 20 years ago!). Malaga is a little further but worth a trip nowadays.
A little further south, Sanlucar de Barrameda or El Puerto de Santa Maria are on the Costa de la Luz and very Andalucian, IYSWIM. Easily reachable if you fly into Jerez and a high probability of some sunshine.
Out of all the above, Seville is great. Don't miss the Alcazar.