I'd say just look for an apartment you like. If you want to be near a park, this could be near the Belgian Parliament (Parc metro station), which is right next to the Parc de Bruxelles (with children's play area), Schuman/Mérode, next to the Parc du Cinquantenaire (in fact in the EU area around Schuman, there's a play area on rue de la Loi next to the CHarlemagne building, and Square Ambiorix and Marie-Louise constitute a little park), around Place Jourdan (Parc Léopold), or further out in Woluwe St. Pierre (Parc de la Woluwe)... However, Brussels is not a large city and you can get everywhere by bus, tram or metro. Wherever you stay you'll be travelling some distance by metro if you want to go out to the Atomium/Mini Europe/Bruparck (children's play area), for instance.
The only "skyscraper world" is around Gare du Nord (plus a single tower at Gare du Midi) which are not areas you'd want to stay be in anyway, but I wouldn't necessarily rule out the city centre proper, where there are of course plenty of shops and cafés.
Most aparthotels/short-let self-catering apartments in Brussels are aimed at visiting executives/officials and priced accordingly. You have Les Citadines at St. Catherine (currently under renovation) or Toison d'Or (http://citadines-toison-dor.hotel-rez.com/index.htm), or try http://www.immobe.be/ but I don't know any agencies specialising in holiday lets. You could look also at http://www.tripadvisor.co.uk/VacationRentals-g188644-Reviews-Brussels-Vacation_Rentals.html