In the pokemon games, there are people who will "rate" your pokemon's happiness. While they don't give an exact number, they tell you what range of happiness your pokemon is in.
"Goldenrod City: A woman in the
house northeast of the Bike Shop will
rate a Pokémon's happiness.
Verdanturf Town: A woman in the house in the south-western part of
town will rate a Pokémon's happiness.
Pallet Town: At Blue's house, Daisy will rate a Pokémon's
Hearthome City: An NPC rates happiness in the Pokémon Fan Club.
Route 213: At the Footstep House, Dr. Footstep will rate a
Pokémon's happiness, albeit in a
roundabout way which differs among
Eterna City: A woman who gives the player the Pokétch App, Friendship
Checker, will rate the happiness of
the player's Pokémon.
Icirrus City: At the Pokémon Fan Club, a member there will rate a
Nacrene City: A woman in the building to the right of the Pokémon
Center with a
rate a Pokémon's happiness."
You can tell what range of happiness your pokemon is in based on the messages below.
"It is super friendly to you! I'm a bit jealous!" 250-255
"It is quite friendly to you! You must be a kind person!" 200-249
"It's friendly toward you. It looks sort of happy." 150-199
"It's quite cute." 100-149
"You should treat it better. It's not used to you." 50-99
"It doesn't seem to like you at all. It looks mean." 0-49
You can also use the Friendship Checker on the poketch.
I assume you are trying to evolve your Eevee into Umbreon or Espeon, so to do that, your Eevee must level up with its happiness at 220 or higher at night or day, depending on whichone you want.