There's a long thread here with lots of good suggestions: http://forum.wordreference.com/threads/accontentarsi-di.86507/
Why don't you take a look at it, and then come back to us with a full context in which you'd say this? Then we can give our opinions on which is the most appropriate translation.
If 'Non accontentarti mai" is a standalone phrase, a kind of exhortation, it might work as something like 'Never settle for second best'.
In some situations, where there is an object, you could use the phrasal verb 'put up with'. A quick search on Italian sites gave me a few phrases like 'Non accontentarti mai di una relazione non perfetta' so here you could say 'Never put up with a second-rate relationship'.
You could also use 'be content' or 'be satisfied' or 'be happy', and you can add 'with + object' if necessary.
Spero di esserti stata d'aiuto.