health testing

where's the best place to get it done?

and what age can it be done

I’m sorry but I don’t quite understand the context of your question.

Are you talking about a health check for acquisition or an “MOT” for a family member ?
For any canine health check, the best place to start would be your veterinary could then send you to specialist referrals if necessary.
The age depends on the reason, I suppose.

Do tell us more about your reasons for the question.

conditions like (L-2-HGA) etc

Ah, ok. I understand better.
You’re talking about the hereditary conditions.

L-2-HGA is tested by buccal swab so test can be done at any age.
You need to run through a laboratory that does genetic screening.

Where are you?

In the UK the AHT used to be the go-to for DNA testing, but I think they've just announced that they're closing.

The easiest way to find out is to contact your nearest Staffordshire Bull Terrier breed club.