Is it legal to open up 2 similar businesses right next to a business because you want to spite the owner?

There is nothing illegal about leasing multiple locations to tenants that operate competing businesses. However, it's not a good practice for a landlord because it increases the likelihood that one or more of those businesses will fail and default under the lease. Savvy tenants often will negotiate a restriction on leasing other space to competing businesses. You should review your lease with an experienced Business Attorney to assess your situation and discuss options.

There is no obligation in law not to rent a place to compete with another business. Mr. Esposito makes a good point about the lease provision available if the same landlord owns all the different properties, but that suggestion only makes sense if you know to ask for it.

Assuming that antitrust concerns are not involved as a matter of public policy, fierce competition is the engine of capitalism. Consult a lawyer in person about whether there are particular factors here that could help you.