Hi GG, near the Grand' Place is a good area to stay in (although note that it's not a palace, the French name Grand' Place = big market square). Have a look at this other aparthotel, Aparthotel Adagio Grand' Place. It is right on top of De Brouckère metro so there is easy access to the metro for the Atomium and Mini-Europe (Heysel). It has a kitchenette and there are a couple of small supermarkets in the streets nearby, but you also have access to Rue Neuve which is a major shopping street and which has a big supermarket in the City2 shopping centre (unlikely you'd need it, the smaller supermarkets are well-stocked). The room itself is simple but nice.
As for the Eurail pass, reconsider it - if you are prepared to plan your trip you can almost always do it cheaper with point-to-point. Trains in Belgium are not expensive and there is no need to book ahead unless you travel with the Eurostar.
Lavandula