If you specifically want a watch, Garmin's Vivoactive 3 is around $100 right now. Has GPS + barometric altimeter and can give you all bike specs you asked for plus climbing data. Also records heart rate, running, hike/walks, exercise, daily steps, etc. if you choose. As a bike computer w/GPS, it runs about 8hrs on full charge. Or it will run several days as a basic watch without GPS, bike-running stuff. I use one for daily running, phone notifications (vibrate) and occasionally for biking. Detailed results on their phone app upload seamlessly to Strava or Ride with GPS once set up.

If you want this only for biking and don't need a watch, the Wahoo Element Bolt is a good choice and gives you turn by turn nav if you upload to it (helps navigate unfamiliar cities if you're touring). Or look at Garmin computers.