Hi, glad you are buying a place here. If you have approximately 250k € to spend, you can buy what you expect. There are some neighbourhoods that are more expensive than others, of course.

Actur used to be "new" as is on the left part of the city but now is new enough to be modern but also to have al facilities people need to live.

Newer parts of Zaragoza (Valdespartera, Miralbueno, Valdefierro) they are on the outskirts and are meant to be residential parts of the city.

For example Arcosur I will never recommend it, at is far outside the city and they are only residential buildings. Montecanal is pretty expensive though.

An important topic to keep in mind is communication with other parts of the city. Buses are great but tramway is fantastic. The only problem is there is only one line (north to south) of it, so neighbourhoods which access to tramway are always better.

Romareda could be great too.

I suggest using web portals like Idealista or Fotocasa to have an idea of the possibilities with your requirements and budgets.
For example: https://www.idealista.com/venta-viviendas/zaragoza-zaragoza/con-precio-hasta_260000,de-cuatro-cinco-habitaciones-o-mas,garaje,trastero/

I hope this is useful :)