It is a shame you are so far away from Weymouth. The train station is a 5 minute walk from the beach.
Exmouth station is walking distance to the beach but personally I prefer Weymouth or Paignton. Went to Paignton earlier in the year. Took me about 10 minutes to walk from the station to the beach - it is a straightforward walk but I am a slow walker.
At Dawlish when I went I found a lovely small beach which had a cafe and toilets nearby. I think it is called Coryton Cove. The train line runs beside the beach and a member of staff at the train station gave me directions to it. I was happy to be quite lazy when I visited Dawlish so spent most of my time on the beach - if you want to be more active I’m not sure what else is around.
Teignmouth station is walking distance to the beach but when I went the tide was in (I know I should have checked tide times beforehand) and I didn’t find much to do.
Hope you have a great trip wherever you decide to go.
Shaldon beach is nice and isn't underwater at high tide, it's reachable by a 5 minute ferry ride from Teignmouth.
I wouldn't recommend going too far into the water though as it's at the mouth of the tidal estray so is going to have quite strong currants.