Here are some recommendations to get your invites printed! Some links below are affiliate, meaning I'll make a small commission if you make a purchase, but this is at no cost to you.
Save 25% with my referral link. Moo is great for extra special finishes and heavier paper weights. They offer 3 different types of paper options, including a glossy or matte finish. Their Luxe paper weight resembles closest to a printed letterpress card.
If you have multiple pieces in your set you need to print, Stationary HQ is a great vendor to have everything printed in one place.
Vistaprint is a great value vendor. They have awesome deals on all of their products, keep an eye out for some here!
Your Local chain: Fed Ex // Staples // Office Depot
This would be a great last minute option, visit a location nearby and chat with them about their options.