L'Shana Tova!
In most synagogues, members can buy tickets for family members, and non-members can also purchase tickets. Usually, family tickets are sold for some nominal fee, while non-member tickets are very expensive (to encourage you to join - as long as you're paying so much for tickets, you might as well kick in a few hundred (or thousand) more and become a member).
A few years ago, when my husband and I were engaged, my ILs invited me to services at their shul; the shul wanted to charge them SIX HUNDRED DOLLARS for my ticket, because I wasn't family yet

, but my MIL badgered them as only my MIL can badger, and eventually they sold me a ticket at the family rate.
For the past couple of years, my ILs (who have since resigned their membership in their synagogue) have come to our synagogue for services. I will see them tonight. (Ughh... pass the Manischevitz...)