The short answer is "probably not".

Long answer:

If you look into it (as a private pilot, you should know "how" already), you will most likely find that there will be a number of obstacles in your path at the majority of large airports.

These obstacles can include (but are not limited to) :

• Airspace restrictions (both local area and at the airport itself) so, for example, you might need IR rating and a suitably equipped aircraft.
• Technical limitations for your aircraft (e.g. your aircraft might not be able to meet speed requirements)
• Airport prohibitions, for example Heathrow publish the following:

Flights for recreational, commemorative, charity and record breaking purposes, light twin engined private aircraft and all light single engined aircraft will not be permitted to use the airport. 'Light aircraft' shall be defined as any aircraft that has a maximum gross take-off weight of 12,500 lb (5,670 KG) or less.

And even if the immediate technical obstacles don't apply, you might find commercial obstacles such as (but not limited to) :

• The requirement to nominate and use a handling agent for ground ops
• Very high landing fees

Generally speaking, the short answer is "probably not" (I don't know Innsbruck).

Long answer:

If you look into it (as a private pilot, you should know "how" already), you will most likely find that there will be a number of obstacles in your path at the majority of large airports.

These obstacles can include (but are not limited to) :

• Airspace restrictions (both local area and at the airport itself) so, for example, you might need IR rating and a suitably equipped aircraft.
• Technical limitations for your aircraft (e.g. your aircraft might not be able to meet speed requirements)
• Airport prohibitions, for example Heathrow publish the following:

Flights for recreational, commemorative, charity and record breaking purposes, light twin engined private aircraft and all light single engined aircraft will not be permitted to use the airport. 'Light aircraft' shall be defined as any aircraft that has a maximum gross take-off weight of 12,500 lb (5,670 KG) or less.

And even if the immediate technical obstacles don't apply, you might find commercial obstacles such as (but not limited to) :

• The requirement to nominate and use a handling agent for ground ops
• Very high landing fees