Does the Box Hill Shopping Centre have a good variety of stores?

While it is small, it does have everything basic you will need.

For bigger shops especially for clothing best go to Doncaster or another bigger shopping centre.

Monique Holgye - Team leader for the Property Management department at Ray White Mitcham

No problems for all your daily needs - plenty of variety of food vendors, and the market is quite good for fresh fruit, vegetables and meats. Asian variety is great, but hunt around and you'll find some other specialty stores, delis, etc.
In the two main shopping buildings there are number of boutiques, but nothing too fancy.
Both main supermarket brands, plus BigW and Harris Scarfe.
If you're on a budget, then there are quite a few low-cost shops in the centres and the mall.

Yes.

Multiple chemists, clothing stores, big w, woolworths, coles, takeaway, dine-in, coffee, kitchen/home wares, etc.

Harris Scarfe was great but it's closed down.

It depends on what you need. If you are looking for Chinese food definitely it is.