How do I determine if a bond is ionic, polar covalent, or non-polar covalent?

No.  You have to use electronegativity.  Although, typically metals and nonmetals create ionic bonds; nonmetals and nonmetals polar covalent bonds; and diatomic molecules pure covalent bonds.

"I know you can use electronegativity....but is there a way to tell by just looking at the periodic table?"
yes. Flourine is THE most electroneg atom on the PT. That being said electronegativity increases as you go diagonally right and up from where the atom Fr is (bottom right corner). thats a prelininary way to gauge electroneg.

If you want to be precise...you gotta look at the electro numbers for the most common atoms and or memorize them (not hard since they got a pattern). Google this.

As for your example they all look polar b/c H is not very electro neg and F and I are very electro neg. Cl as well.

The only sure way is to subtract the electronegativities of the elements. But generally, we can use the periodic table in a limited way. The further two elements are from each other on the table, the greater the likelihood the bond between them is ionic. Remember that elements on the left of the table are metals and tend to give away (or offer for sharing) their electrons. Those on the right are nonmetals and generally take (or try to anyway) electrons.  Elements in the first 2 columns (groups 1 and 2) that react with elements in 16 and 17 are generally ionic. If the metal is near the top of the table and the nonmetal is toward the bottom, we'd have to check electronegativities. The most electronegative elements are fluorine first, oxygen second, chlorine third, nitrogen fourth; the most electropositive are
Francium, Cesium and Rubidium but we seldom see these elements in compounds.