expression
if you prefer; if it would be better; if you need
Polite conditional expression used to offer a choice or suggest an alternative. Often follows a noun or verb phrase with の/こと, e.g. こちらの方がよろしければ (if this one is better for you).
お車でお越しになる方がよろしければ、駐車場をご利用ください。
If you would prefer to come by car, please use the parking lot.
こちらの日程の方がよろしければ、ご連絡ください。
If this date works better for you, please let us know.
方がいい is a more direct and casual suggestion ('should'), while 方がよろしければ is a polite conditional offering a choice.
よろしければ alone means 'if it is all right' and is used for permission or polite requests, whereas 方がよろしければ specifically compares options.
Phrase composed of 方 (ほう, 'direction/option') + が (subject marker) + よろしければ (polite conditional of よろしい, 'good'). Literally 'if this option is good'.