Being an old native Floridian where it appears the tacky tourist souvenir came about 100 years ago, I avoid everything made for tourists or sold in souvenir stands. But there are many great alternatives.
Every community has a boulevard with shops that cater to locals. Is is San Rafael in Havana. But they are all over. Buy something really Cuban made for Cuban use. Like a cast aluminum soup ladle or a clothes pin bag. Lots of uniquely Cuban things there. And, always dirt cheap since everything is for the Cuban, not tourist, market.
Find a religious articles store. Your own personal religion makes no difference. Buy a Santeria doll or one of those painted eyeballs with the tongue sticking out of it and a sward piercing the tongue with dripping blood. They are hung by the door to keep evil spirits from entering.your house (mine has been quite successful at that for years) Again, dirt cheap as priced for Cubans, not tourists.
Plaza de Armas in Havana has many vendors with a huge selection of classic Cuban books and antique memorabilia. Priced for tourists but still reasonable. Some real treasures buried in with much junk..
There is Cuban art both 2D and sculpture make for both the tourist market and legitimate art. Cuba has some incredible artists but their work is priced by international standards.
The Magnum Opus of places to bring something of significance home is Ediciones Vigia in Matanzas. This small workshop creates hand made books, often on hand made paper, in editions of not more than 100. These are not ordinary square books with a series of pages. They are multi dimensional irregular shaped pieces of art made in the workshop there by an handful of artisans. 25-35 CUC is a steal for a hand made artisan book.
We traveled from Havana to Matanzas just to go to Ediciones Vigia. My sister was visiting and wanted something special to take home and my Cuban significant other from Holguin had heard of it but never been. She manages a library system and has a significant personal classic book collection. She is also a published poet and they recognized her name. So we got the royal tour including access to previous editions that ordinarily were not for sale. It turned out to be an expensive day but well worth it.