- welcome, tsbalja.
'I want someone to choose...' But the way you use adjectives is unusual - not out-and-out wrong, but hard to understand in this context; well, 'the convenient one' is not wrong; 'the suggested' is, though 'choose from those suggested' would be OK in formal writing. And 'at your convenience' sounds very formal - which is not what you want.
So I think you need to break your text up into two sentences - something like
(I am among those teachers who don't mind starting a sentence with 'But'. In informal writing, though, I don't think anyone would object. )There are lots of good cafés and other places to choose from, and I suggest any of these: ...<your list>. But it's up to you; you choose whichever one suits you best.