From Gare du Midi take the train to Gare Central (5 min) and have a short walk. The HI is in the center of old town Brussels, therefore sightseeing is an easy walking thing.
Everything else depends on what do you prefer. The metro system is easy to come by (and cheap), busses and tram are a bit more tricky but generally you can visit more or less every area of interest within 30 min by public transport.