Our suggestions
Instead of 'accessible' we suggest you use:

(you can) get it, get to it, get into it, use it, take part in

There are a number of ways you can use our suggestions, depending on what you mean. For example, instead of:

'make sure your health card is accessible' you can say 'make sure you keep your health card where you can find it', or ' . . . within easy reach', or '. . . where you can get to it'

or, instead of:

'so that your garden is accessible', you can say 'so you can get into your garden', or 'so your garden is easy to get into'.

As well as the usual meaning of 'accessible', in the sense of something you can get to or get into, people now use it to mean 'available to all'. When writing to non-experts it is better to avoid this usage. For example, rather than talk about 'accessible healthcare' it is better to talk about the groups you mean 'getting the healthcare they need' or 'being able to get proper healthcare' and so on.