How sweet. Budgies are such social birds. Below is some info for you about outdoor and indoor plants.
This lists both toxic and nontoxic plants in alphabetical order.
http://budgieplace.com/plants....
this from the link below:
Safe Houseplants
Nibbling on houseplants can provide nutrients for budgies, so all the plants in the home should be nontoxic to birds. Common houseplants that show up consistently on “safe-plant” lists for birds include African violet (Saintpaulia inonantha), which is hardy outdoors in U.S. Department of Agriculture plant hardiness zones 11 and 12; jade plant (Crassula argentea), hardy outdoors in USDA zones 10 and 11; spider plant (Chlorophytum comosum), a perennial in USDA zones 9 through 11; and peperomia (Peperomia spp.), hardy outdoors in USDA zones 10 and 11. These plants are of course grown indoors across all zones.
http://homeguides.sfgate.com/k...
These are flowers that Budgies find tasty...and they are safe.
http://www.birdchannel.com/bir...
Hope this helps.
