The rules say
Finally, each player scores one point for each
Tourist Attraction that is connected to one or more
of the Routes they claimed.
In your example, there are three Tourist Attractions connected to at least one your routes, so you get three points from Tourist Attractions.
You are never required to obtain additional destination tickets cards, even if you've completed the ones you have.
You have three options available to you:
You could claim a route. Remember, routes are worth points, and nothing prevents someone from claiming routes once their destination tickets have been completed.
You could pick new destination ticket ...
No, you do not have to claim new destination cards. There are other options available, such as claiming routes to block others or pick up the points.
Deliberately aiming to complete the minimum destinations early and claim routes arbitrarily to block the opponents can even be a viable strategy depending on what you first pick up at the start of the game.
Starting with the youngest player and proceeding in clockwise order,
players take turns until the game ends. On your turn, you must do one
(and only one) of the following three actions: draw Transportation
cards, claim a Route, or draw Destination Ticket cards.
There's nothing ...