Good place to see fighter jets near Moscow KUBINKA Air Force Base

I do not know the regulations off-hand, but I would recommend posting your questions on one of the many spotting communities - ruspotting.net; livejournal.com->ru aviation, etc.
The biggest resource (Russianplanes) has recently been taken offline, I don't know where all the regulars moved.

Careful you don't get arrested for espionage, especially in Russia. Taking photos of active military equipment has tripped up more than a few tourists.

Exactly. Also, security will be ramped up for WCup, and safety/security regulations are likely to be very strongly enforced.

ETA: according to this blog (https://alexbabashov.livejournal.com/47678.html), Kubinka has an official spotting area, but it is less than ideal.

Dear Perilofp, Sam and Emma,

I think i will change my mind to cancel photo taking on any active military equipment/ establishments after got valubale information from all of you.
Thank you all so much.

Simon

https://ru.usembassy.gov/u-s-citizen-services/russian-visas/

Restricted Areas

U.S. citizens should be aware that there are several closed cities and
regions in Russia. Travelers who attempt to enter these areas without
prior authorization are subject to arrest, fines, and/or deportation.
A traveler must list on the visa application all areas to be visited
and subsequently register with authorities upon arrival at each
destination. Travelers should check with their sponsor, hotel, or the
nearest office of the Russian FMS before traveling to unfamiliar
cities and towns.

There are two recent high-profile cases of people interested in military hardware movements being detained and/or extradited.

One involved a rather well-known Western spotter who was detained while photographing at one of the military airfields. Not sure about the particulars of the case - or the outcome, for that matter, - but he seems to be back online posting airplane photos, so I assume he was released.

The other one was a couple of British diplos equipped with a radio scanner and photo equipment enjoying the great outdoors near another military airfield somewhere in Dagestan. This case was a bit more clear-cut precisely for the reasons cited by Edgar above - the whole area was designated restricted, and the two gentlemen didn't have clearance or permit. Luckily for them, they had diplomatic immunity.

Hello again Simon, how did your trip go?