I would highly recommend an HP Spectre x360 from personal experience if you're looking for a Windows model. It has a solid build and will fit in your price range pretty well depending on the specs you get. I'd just suggest making sure you at least get an i7 and 8gb RAM. http://www.bestbuy.com/site/hp-spectre-x360-2-in-1-15-6-4k-ultra-hd-touch-screen-laptop-intel-core-i7-16gb-memory-256gb-solid-state-drive-natural-silver/4864800.p?id=bb4864800&skuId=4864800
Theres a good model that should fit all of your needs. If you're looking for any other suggestions then the Lenovo Yoga 900 has been very well received as well. Other machines could include Macbook 2016, Macbook Air, or Macbook Pro 13 if you like MacOS, or if you want more Windows recommendations then my 3rd pick would be a Toshiba Satellite 13in series. I could also recommend a Dell XPS 13, but I have very bad experiences with Dell so proceed with caution.