If I understand correctly, this should be a fairly straightforward analysis, though there are a few ways you could approach it.
You could use the Raster to Point tool in the Conversion toolbox.
in_raster = [Your land cover dataset]
out_point_features = [Designate an output feature class]
raster_field = [The value field that holds land cover values in your dataset]
Then you have a "grid-looking" point feature class (may be a bit resource intensive depending on the size and spatial resolution of your land cover dataset) that you can then do a select by attribute or a SQL definition query on to limit the dataset to just the land cover values you want.
If you already have a point feature class that you want to use to grab values, and you have access to Spatial Analyst, use Extract Values to Points in the Spatial Analyst toolbox.
in_point_features = [Your pre-made point feature class]
in_raster = [Land cover dataset]
out_point_features = [Designate an output point feature class]
optional fields: Should be able to ignore these unless your needs dictate otherwise.
Again after you get the output you could use a select by attributes or SQL definition query to pull out only the values you want.
Conversely if, for some reason, you need to limit the land cover values before you extract them, you could use the Con tool in Spatial Analyst to return the values you need, then use one of the above methods.
Hopefully one of those two solutions helps.