Are there any Indian restaurants in the city?

There are lots! Maya Masala on Market St opposite Central Market, Harvest of India and Beyond India on O'Connell St, as well as at least one on Melbourne St and one or two down Rundle St that I don't know the names of.

British India on Gouger Street in nice and I like the decor too

There used to be one off of Hindley Street, in a side alley and downstairs. They had the most amazing Butter Chicken! I also love Beyond India in North Adelaide, who are definitely still there in O'Connell Street.