Courgettes will do fine outdoors but don't plant too many - you'll get throroughly sick of cooking them, eating them and eventually your friends and neighbours will disappear indoors when they see you approaching with courgettes in your hand.
Nice! They will however also grow into marrows (same plant) which are lovely stuffed with bolognese, but you also done need to many of those.
Carrots are not hard to grown, but need soil without stones, if you want them to look nice. Parsnips are also nice if not murdered by the cook.
I have yet to really do any veg growing, but my parents grow Swiss Chard which eats well and appears fairly bomb proof and seems to grow right into early winter and a cut and come again basis.
Lettuce is also a good shout, and Rocket; which all but grows itself. Radish seems easy but I dont like the taste.
They also do cucumber/gerkins, which I have done once in one end of my conservatory in a large pot using there excess seedlings and that worked very well even with a few cock-ups on the watering and feeding (with tomorite), but I think like Tomatoes they are basically greenhouse/polytunnel/conservatory thing.
I think they have now given up with growing Tomatoes from seed as far as I know, having had a few years of them not coming up, favoring 6inch tall garden centre plants as a 'plan a' option rather than a rectification strategy after the buggers haven't come up again!
They also grow sweetcorn to eat as 'corn on the cob' as its soooo much nicer fresh than 24h old from shops. But you need about 12ft square for it to stand up to the wind. I dont know how well it would work in a sheltered (but not shady) corner?
Mangetout peas are also nice to eat. Pick something you like eating.
Daniel