London

Here's an ideal itinerary for 3 days in London that meets all your constraints:

Day 1:

• Start your day with a hearty vegetarian breakfast at The Breakfast Club in Soho. They have a great selection of vegetarian options, including their famous veggie breakfast.
• After breakfast, head to Hyde Park, one of London's largest and most beautiful parks. Take a stroll through the park, enjoy the greenery and the fresh air.
• Next, head to the Natural History Museum, which is located right next to Hyde Park. The museum has a fantastic collection of exhibits, including a life-size model of a blue whale and a dinosaur gallery.
• For lunch, head to Mildreds in Soho, which is a vegetarian restaurant that serves delicious food. They have a great selection of vegetarian and vegan dishes.
• After lunch, head to the British Museum, which is one of the world's greatest museums. The museum has a vast collection of artifacts from around the world, including the Rosetta Stone and the Elgin Marbles.
• For dinner, head to The Gate in Hammersmith, which is a vegetarian restaurant that serves delicious food. They have a great selection of vegetarian and vegan dishes.

Day 2:

• Start your day with a vegetarian breakfast at Dishoom in Covent Garden. They have a great selection of vegetarian options, including their famous breakfast naan.
• After breakfast, head to Kew Gardens, which is a botanical garden located in southwest London. The gardens are home to over 30,000 different kinds of plants and trees.
• For lunch, head to The Duke of Cambridge in Islington, which is a vegetarian pub that serves delicious food. They have a great selection of vegetarian and vegan dishes.
• After lunch, head to the Tower of London, which is a historic castle located on the north bank of the River Thames. The tower has a fascinating history and is home to the Crown Jewels.
• For dinner, head to Mildreds in Camden, which is a vegetarian restaurant that serves delicious food. They have a great selection of vegetarian and vegan dishes.

Day 3:

• Start your day with a vegetarian breakfast at The Good Life Eatery in Chelsea. They have a great selection of vegetarian options, including their famous avocado toast.
• After breakfast, head to Regent's Park, which is a beautiful park located in central London. The park is home to the London Zoo and has a boating lake.
• For lunch, head to Tibits in Mayfair, which is a vegetarian restaurant that serves delicious food. They have a great selection of vegetarian and vegan dishes.
• After lunch, head to the Tate Modern, which is a modern art museum located on the south bank of the River Thames. The museum has a fantastic collection of modern and contemporary art.
• For dinner, head to The Gate in Marylebone, which is a vegetarian restaurant that serves delicious food. They have a great selection of vegetarian and vegan dishes.

I hope this itinerary helps you plan your trip to London!