Veg travellers won't have any problems in Phnom Penh as the city is full of vegetarian and veg-friendly restaurants. Here are the ones I liked the most.
Veg Café soleil was by far my favourite. It has an extensive menu, mostly vegan. They use fresh and good ingredients and their meals are light and balanced. But be careful, portions are quite big, so it's better not to order to much (even though sometimes it's hard to resist the temptation to try everything!).
The address is #22DEo, street 278, Boeung Keng Kang. It's parallel to Preah Sihanouk Blvd (274), between street 57 and street 63. It's not far from the Independence Monument. Its facebook page is: http://web.facebook.com/pages/Cafe-Soleil-vegetarian-restaurant/243816902304334
The Visitor Centre of Daughters of Cambodia is definitely worth checking out. It has a cafe, a spa and a fair trade shop. The cafe is very vegetarian friendly but options for vegans are quite limited. Anyway, the avocado, pumpkin and spinach salad we had was really good.
The address is #321 Sisowath Quay, on the riverside near the National Museum. Here's their website: www.daughtersofcambodia.org/visitor-center
The Corn is not a vegetarian restaurant, but all recipes are vegan unless you decide to add non-vegan ingredients. With their philosophy they really made the life of veg travellers much easier!
It's in 26 Preah Suramarit Blvd, near the statue of king father Norodom Sihanouk. Its facebook page is http://web.facebook.com/thecornphnompenh/?_rdc=1&_rdr
The NGO TREE Alliance created two training restaurants for street children in Phnom Penh: Friends and Romdeng. They're both very veg friendly and they serve very creative food. Whether you're interested or not in their social project, it's definitely worth going there simply for the great food and atmosphere.
They're both in very good locations. Friends is in #215 Street 13, near the National Museum. Romdeng is a 10-minute stroll away, in # 74, St 174.
This is the complete list of TREE restaurants in Cambodia: http://tree-alliance.org/our-restaurants/our-restaurants.php?mm=or
And the picture below shows the beautiful setting of Romdeng. If you go during the day you can also go for a swim!
A very nice place for lunch or coffee is ARTillery Cafe in an alleyway of street 240. Just make sure you don't miss the alleyway as it's very easy to get distracted by the beautiful boutiques and shops of street 240!
They have many good and creative veg options. You can check the menu on their website: http://artillerycafe.com Vegetarian and vegan meals are clearly labelled.