Sorry, but the forum ate my reply so I'm going to be brief.
Pretty much all of them, except for the military and the FBI. Congress and the federal government is prohibited by the Constitution from operating within the states. It can only operate within the territories and possessions owned by the federal government. I give you Article I Section VIII Clause XVII-XVIII and Article IV Section III Clause II.
To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings;--And
To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof.
The Congress shall have Power to dispose of and make all needful Rules and Regulations respecting the Territory or other Property belonging to the United States; and nothing in this Constitution shall be so construed as to Prejudice any Claims of the United States, or of any particular State.
Congress and the federal government has so little to do that the Constitution specifies that it must meet once a year. This is part of the Constitution because the author's were afraid that a Congressman would actually forget to show up. I give you Article I Section IV Clause II.
The Congress shall assemble at least once in every Year, and such Meeting shall be on the first Monday in December, unless they shall by Law appoint a different Day.
The categories I listed were:
Welfare programs
Federal law enforcement
Defense spending
Disaster response
Transportation infrastructure
Public education
Regulatory agencies
You've admitted that defense spending is constitutional and so is the FBI. So let's go over the other things mentioned.
The FBI covers general law enforcement. However, we also have the ATF, DEA, and Secret Service (when they also covered counterfeiting under the Treasury Department) and other similar agencies that focus on specific policies of federal crimes.
Also, public transportation infrastructure could be construed as a part of defense spending. After all, Eisenhower called for the building of federal highways so that the military would have a rapid deployment capability in case of a military emergency. The fact that the federal highway system has also helped out commerce and citizens is an exceptional bonus. And let's not forget that our nation's waterways also qualify into that.
Then there are the things that are obviously constitutional but you didn't mention.
These are regulatory agencies, such as the SEC, the FCC, the FDA, the EPA and the like. These are constitutional because of Congress' ability to regulate interstate commerce. This allows Congress to pass laws making certain business practices illegal and allows them to protect the people of the nation. Businesses can engage in unfair or unethical business practices that hurt their customers nationwide. Such regulatory agencies allows the federal government to prevent businesses from engaging in such abuses.
Then there's welfare spending, disaster response, and public education. While you do not recognize these aspects under the clauses you mentioned, it could be argued that the federal government has the power over these areas in order "to promote the general welfare" stated elsewhere in the Constitution. Welfare programs promote the welfare of the elderly, the disabled, the unemployed, children, and the poor. Disaster response services promote the welfare of those who are victims of natural disasters, especially those that occur over state lines or overwhelm the resources of local and state governments. It could also include national security if it is a terrorist attack. Public education promotes the general welfare by giving all American citizens a basic quality of education and socialization. If we want Americans to follow the laws of our country, we have to teach them the skills to because a basic citizen of our country. However, I understand that because it is not specific, conservatives have a big problem with this clause.
Now you and I may agree in that not all of these programs work as best as they should. I fully admit to that, and I'll be the first one to say that our government agencies require reforms.
However, my contention is that such government programs are not only constitutional, but necessary in order to have a secure, flourishing nation.