We are planning a one week visit to finish our trip off in Europe. I am not sure exactly which city we will base ourselves out of as of yet (Most likely Brussles or Ghent) but is it best to just book a hotel or can you rent a apartment for a week? Do they have VRBO ( vacation rentals by owner) ?
All of your ideas are options. You can stay in Brussels, Ghent, or any other city; you can stay in a hotel or apartment; if you want an apartment, you can use VRBO, Airbnb, or other sources.
Which is "best" is determined by what kind of place you prefer to stay in, and by personal taste in the various cities (which you won't know in advance). The subject of how people feel about the various Belgian cities is very contentious. I personally loved Antwerp, liked Bruges, was slow to warm to Ghent but liked it in the end, and found Brussels uninspiring, except for the wonderful Art Nouveau tour from ARAU: http://www.arau.org/en/tours. But that's my personal opinion, not objective fact. Each of these can be seen from a base in the others as a day trip, so you aren't restricting yourself by staying in any of them.
Rick's books that include Belgium (Amsterdam, Brussels and Bruges and Snapshot Brussels and Bruges) now include Ghent and Antwerp as well, so you can read his impressions of all of them.
Like Harold I loved Antwerp, don't see why so many people don't like it. I also loved both Bruges and Gent but for different reasons. All three of these cities are worth seeing and spending a day or more in. I stayed in Brussels and did the other 3 as day trips and that worked well for me. I liked Brussels as a base, enjoyed walking to the train station each morning through the Grand Place to get the train for my day trips, watching the flower sellers get set up, stopping for a warm fresh waffle (or croissant) to start the day. I also enjoyed the bustle of Brussels in the evenings. I stayed in a hotel in Brussels so don't have any advice about an apartment.
No apartment advice but I stayed at a lovely B&B/Hotel in Brugge for four nights last winter. PM me if you are interested.
Best is not a useful term. You appear ("VRBO") to care about price and food budget. Did you mean to write "cheapest"?
I stayed for a week in the Hotel Lucca in Bruges. It was about 2 or 3 blocks from the main square.
I found Bruges a great place to do so many things, canal tour, rented a bicycle and rode out to see the windmills, went to the top of the main square tower, ate lots of chocolate, took
one day train trips to Brussels, Ghent, and the coast of Flanders.
You can also see the famous Michelangelo Madonna that was featured in the move
"Monuments Men" in Bruges.
I suggest Brugman court apartment in Brussels you can find either on VRBO #336932 or on www.whitehousevactionrentals.com
If you want a hotel, Motel One in Brussels is great!