My textbook (Minna No Nihongo I ch. 22) gives:
私がいつも買い物するスーパーは野菜が安いです
(The supermarket I always do my shopping at has cheap vegetables (for sale)).
I'm guessing this is ok actually, and it might be better than
私がいつも買い物しているスーパーは野菜が安いです
(The supermarket I'm always doing my shopping at has cheap vegetables (for sale)).
However when I solved it I rather wrote:
私がいつも買い物に行くスーパーは野菜が安いです
(The supermarket where I always go to do my shopping has cheap vegetables (for sale)).
But now I'm doubting this a little (such is the nature of the very immature student of Japanese, without tutor): maybe the -iku actually modifies the noun too much in the "traveling" sense of "to go", and this does sound a little off?
Maybe Japanese just say
いつも買うスーパーは野菜が安いです
Although this may sound like I always buy the supermarket.
I feel like I will learn a lot by just asking this and asking for the best type of nuance, because noun modification is a little scary in that I don't know how the end result might feel like.