Basil is hopeless outdoors for me but does well on a windowsill. Always water it from the bottom as it doesn't like its leaves wet - they just go rotten. You might want to try some Thai basil which has a very different flavour and don't forget about cress - up in a few days on the windowsill.
You could also try some pea shoots on the windowsill. In a deepish pot plant the peas shoulder to shoulder and cover with compost. When the shoots come up cut the whole thing and eat them. They taste like fresh peas.
