If your wife is a citizen of Spain, she has EU rights and if you are legally married so do you.
If your wife is from Spain but does not have a current passport, it would be worth your while to check with the local Spanish consulate wherever you are to see what she needs to do.
Reopen.europa.eu is the excellent, up-to-date website that gives the official information about rules for entering and traveling given the pandemic situation. Make sure you check that page.
There are many apartments available for rent in Brussels -- plenty of vacancies -- and you will want to look in the more highly-rated residential neighbourhoods: Uccle (Ukkel), Ixelles, Saint-Gilles, Salon... These are places you can readily get by without a car because shops are so abundant and conveniently situated. Apartments tend to be less expensive than in London, Paris, Amsterdam and any major US city; about as affordable as they are in Canada.
When I found an apartment I wanted to take, I did not have a Belgian bank account. You will need one to take a longer lease. The manager ("syndic") of the apartment took me over to her own banker and they set me up, using my US information, so I could take the apartment. Everyone was very courteous and spoke excellent English. Brussels is a very international city; plenty of people speak English. French, Dutch and Flemish are of course the more commonly spoken local languages, but even utilities and phone companies provide customer service in German, in many cases, as well.
I found the process of settling into Brussels easy. The city is charming; it is a wonderful place for people with a penchant for gourmandise -- a lot of fantastic food available, including Mexican, Argentinian, Brazilian, Moroccan, Russian, Greek, Turkish, Iranian, Indian -- really a huge range. One of our favourite haunts is "The Everest", a Tibetan/Nepalese/Himalayan restaurant with amazing authentic cuisine. If you are someone who doesn't mind walking, or cycling, Brussels is small enough to traverse on foot and get to know well. And of course the public transport is outstanding.
There are legal advisors available, and they are not expensive, to help you navigate the registration process if you decide to formally become a Belgian resident. Post-Brexit, people from the UK (as one example) have to pay special attention to the registration rules because of reciprocity (UK is still not helping all Europeans who wish to remain in Britain, so there is an equivalent expectation that Brits coming to live permanently in Belgium need to comply with the formalities. However, these are not difficult, nor are they expensive. Our oldest son got it all done quickly in good time, just by visiting the local municipal office. Brussels' municipalities are called "Communes" and it is there most of the official registration and documentation issuance takes place. (As with local Councils in UK, for example.) If you do not require public assistance because you have independent means or a source of income, you will find it is not difficult, and indeed it is highly rewarding, to make Belgium your home. Cities outside Brussels are for the most part even less expensive for renters as well as home-buyers. The culture is specific and lovely, but you will find people tend to be helpful without being nosy or prying. And the location cannot be beat: close to everywhere. Excellent air and train connections, plus buses for those who don't wish to drive themselves.