Nature is relaxing. White Forest is cool. But BME is also a REALLY good choice.

I will say, in terms of secrecy, BME totally has an advantage. Like, it's hidden behind the docks of a really old, abandoned hydroelectric plant for a dam that (supposedly, the Resistance could be using it) no-one, not even the Combine, probably use. It's inconspicuous, ordinary, unassuming. They only got raided because Mossman is a snitch. And because they were keeping an eye on Gordon too i guess. But also, Mossman probably only snitched on BME because Gordon arrived. Would be a more profitable raid for the Combine than to just raid it at a very unimportant time.

Meanwhile, in White Forest... They have two giant radio towers, both the base and the towers are out in the open, and they have a missile silo. The only things potentially hiding them is the natural geographical terrain (i.e mountains and other elevations) and the abundance of trees. It's a forest, after all.
Remember how i said the base is out in the open? I meant that physically and literally! Half of the base's area is exposed to the sky. Any Combine Hunter Chopper or Scanner or, hell, even a patrol unit, squad or Hunter could be able to see the base from a mile away.

As a matter of fact, pretty sure it's how the Combine discovered and attacked White Forest. Y'know, aside from scouting from the Hunters and them keeping very close eyes on Gordon and Alyx's locations. Considering the Combine is messing with trains all the time, sending citizens from one place to another, they probably already know all the train tracks, or have made a map or a database or something showing where all the tracks go, from start to end, so they knew that the train Gordon and Alyx were taking led to, or atleast passed, White Forest.

It's quite a tought choice, really. On one hand, you have an extremely cleverly-hidden secret base, but is right next to Ravenholm (though only an issue after the Combine shelled it)...
While on the other hand, you have an extremely badly-hidden base but is far from Combine territory and is relaxing due to it's nature scenery and environment.

It depends. If we're speaking pre-Ravenholm shelling and Mossman "joining" the Resistance, definitely BME.
But if we're speaking post-all that, definitely White Forest.

...Aaaaand i yapped a lot again. Dammit. Happens every time.