I'm from Mathura. . .
it's good place to celebrate holi their with friends but I will not suggest you to go along with girl in holi time because it's not that much safe, in Mathura whole city celebrate holi together and you can't stop anyone to put colour on yourself meanwhile sometimes misbehave also used to do by some people.
It's a great experience and you'll enjoy Holi there. it'll be very good and colorful. I just want to suggest you whatever you say the people there won't leave until they put color on you and the people are nice and that's the culture there during holi
so it's advisable to wear waterproof clothes and protect your skin, hair and also your mobiles from colour water. you can roam near banke-bihari Temple and can roam through the streets on that auspicious day.
you can also go for vrindavan parikrama hope it helps!!