Brief Answer:
Betahistine, piracetam, flunarizine

Detailed Answer:
I read your question carefully and I understand your concern.

Dizziness after stroke is difficult to treat. Even if meclizine didn't cause side effects its efficacy is more limited in stroke patients, it is more effective in balance issues with a vestibular origin. I would say that the most recommended remedy is physical therapy with balance exercises assisted by a physical therapist.

Regarding medication an alternative to meclizine is a substance called Betahistine. I believe in the US it is sold over the counter under the brand name of Serc.
Piracetam is another possibility to consider, mostly found under the brand name Nootropil, but there may be other brands as well.
Another alternative is Flunarizine, but while very popular in Europe I believe it is not present in the market in the US where you seem to reside.

I remain at your disposal for other questions.

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