Learn Italian: La banca è su questo lato della piazza. - The bank is on this side of the square.

You could use al di qua della piazza. The complex preposition al di qua di means "on this side of" and is a great, natural-sounding alternative to the literal su questo lato di. If the bank were on the other side, you would use al di là della piazza.

Is there another common way to translate "on this side" besides su questo lato?

Yes! Italians very frequently use the word parte (part/direction) instead of lato. However, parte requires the preposition da, making the phrase da questa parte della piazza. Both su questo lato and da questa parte are perfectly correct and widely used.

Why does su stay separate here instead of combining into a word like sul?

As a quick refresher: Italian prepositions only fuse into single words (articulated prepositions) when they meet a definite article (like il or lo to make sul or sullo). Because questo is a demonstrative adjective and not an article, the preposition su must remain a separate word.