Путешествовать - travel in general, no matter what means of transport.

Объехать (and also объездить)- technically implies travelling by something with wheels or rails (though contexts may vary), and it usually means thourough and extensive travelling within a particular location. Examples: Мы смогли за одно лето объехать почти всю Италию (we travelled a lot in Italy and visited a lot of places there this summer, does not necessarily mean we were not taking flights there).