Blaster Master
A game that does have quite a good quality and soundtrack, You use a certain kind of futuristic tank and destroy enemies all around. It is a NES game that did not have that much future but at least we can say there are some fans about it.
Sky Shark
A shooter game that does have lots of good music and a fast paced game action. It is quite interesting and I do like the intro soundtrack a lot, it uses that repetitive sort of instrument that I enjoy a bunch. One good game that you could play.
Crystalis
Another great game that is a little lot like the Legend of Zelda. You could say it is very similar but it has its own features. I really liked this game a lot, it is post-apocalyptic and very interesting to play. Music is awesome as well and it came to me in a very important moment of my life, when I met Jesus Christ.
Startropics
A great game that I really did not play that much but i recognize it is good. It has to do with a guy that lives in sort of a Hawaii island but there are lots of monsters and you have to go on an adventure. It is great in music as well.
Castlevania II: Simon's Quest
It is a cryptic game and it is not particularly awesome but it does have a great soundtrack. I know it is weird to include it in this list but you could say that it has quite good design as for graphics, but that tornado part is just terrible.