Invisible braces can be of multiple types. ..lingual braces that are placed on the inner surface of the teeth , transparent removable aligners and less visible ceramic braces.  However the ceramic braces will  have some element of visibility. There are multiple orthodontists in the city who would be able to provide you with these options. Best hospital is a very subjective  opinion. .It is best to choose a place where the orthodontist is available on a daily basis rather than a hospital / clinic where they visit occasionally. You may have to visit a few places to decide what works best for you and the cost of the treatment also varies between different orthodontists and hospitals . Another element of pricing variability comes with the degree of complexity of the alignment problem. A clinical consultation is the best way forward.