Rome to Rio (https://www.rome2rio.com/map/Budapest/Agordo) does a good job at this particular example and even found a bus connection from Treviso to Venice to Agordo which may be easier than they train connection.
Another good tool for "rough" planning is www.flightconnections.com which is map based. You can quickly see that the nearest airports to Agordo are Bolzano (BZO), Treviso (TSF) and Venice (VCE). By clicking on the dots, you will see that only Treviso (TSF) has a non-stop connection to Budapest (Ryan Air and Sundays, Wednesdays and Saturdays).
Once you have identified the best airports you can use an advanced flight search tool like ITA Matrix https://matrix.itasoftware.com/search to look for flight options. This tool has A LOT of options and you can build very complex queries including arrival, airlines (include & exclude), max layover, total travel time, multiple airports, etc.
Unfortunately ITA Matrix doesn't cover budget airlines like Ryan Air, so if this is an option you may have to search on sites like momondo.com or https://www.azair.com/ (which allows also multiple airport and date ranges).
Once you have a viable flight options, you can use rome2rio or even google maps to quickly check public transport options from the airport(s) to your final destination.
At the end you still will have to manually stitch it together. Unfortunately, even train tickets have been become very complex: Deutsche Bahn offers 5 or 6 different ticket types for each trip with different rules and restrictions.
In general you will not find a website that can accommodate sand rank all of your preferences since this is just too complicated. Choosing travel involves very complex trade offs between convenience (depart time, arrival time, #of transfers), price, overall time, mode of transportation, flexibility, refundability, baggage, etc. Each case is different and some preference are also deeply personal. The fastest connection doesn't help if it arrives an hour later than you need to be there.
There used to be flight search site called hipmunk.com which sorted options by "agony" which was trying to estimate this trade off. Unfortunately they were too good at it so they got bought by Concur (American/Express) and shut down.