I have read it a few times and it does not permit the tenant to talk to other municipalities without the permission of the St.Pete City Council. Here are two excerpts:

It says," Section 8.03. Remedies. The CLUB and CITY agree that neither has an adequate remedy at law for breach of this Agreement. The CLUB and CITY agree that, in the event of a violation of this Agreement, the party not in default shall be entitled as a non-exclusive remedy, and in addition to an action for damages, to seek and obtain an injunction or decree of specific performance or an equitable remedy from a court of competent jurisdiction to enjoin or remedy any violation of the Agreement. In the event a court refuses to grant specific enforcement of Section 2.04, the parties agree that one element of the damages to be considered by the court as having been incurred by the CITY for a breach of Section 2.04 would be the outstanding bond debt at the time of the breach on those bonds backed by the Franchise Funds. and negotiations (directly or indirectly) for the use of any facility other than the DOME for the Home Games of the Franchise except to the extent permitted by Section 2.04. The parties recognize that any violation of this provision will result in irreparable harm and damages that are not readily calculable. Accordingly, as a non-exclusive remedy, in addition to any damages that may be deemed to be appropriate, the CITY and the CLUB acknowledge that each party shall be entitled to injunctive relief in the event of a violation of this Section by any other part.