You might like Brian Conrad's handouts. Specifically, Construction of tensor products and the two handouts after that one. They have a heavy emphasis on the universal property and examples.

(I don't think this warranted more than a comment, but I can't post those yet.)

You might like Brian Conrad's handouts for a sophomore differential geometry course. Especially relevant are Construction of tensor products and the two handouts after that one. They have some nice examples and a heavy emphasis on the universal property.

(I don't think this warranted more than a comment, but I can't post those yet.)