June is perfect
lovely sunny days and the evenings are warm! Food wise if you eat local it's cheap.... Transportation wise you can take the bus when you go out of Amman (cheap, and works well though have never tried!! - but know loads who have) taxis are also very available - and cheap Wwhen in Amman - just make sure they put the meter on... Even when you leave a tourist attraction. Specially thinking about the citadel, might be worthgoing of site and find a taxi or walk down to downtown - i believe there are some steps so ewhere. (there is a post on here somewhere about taxis). Tourist attraction is what you really need ro budget for. Petra for ex. Is 50jd for the day! Jerash around 7-8, public beach at the Dead sea is 16 or 20. Hope it helps a bit. Please read my blog if you want ideas on what to see... Hope it helps a bit