Budget cuts

Cabinet departments.
End agricultural subsidies (this is about 30 billion)
End trade barriers on agriculture (sugar and milk are the most well-known of these).
Basically just abolish the department of agriculture and leave the USDA's food safety system in place (and consolidate the USDA and FDA mandates and departments into one branch rather than spread all over like some grotesque word salad of rules)
Abolish the vice presidency and any duplicate functions of the executive branch associated with the bureaucracy for this position. I've already outlined my presumed method of replacement should the president be assassinated, killed, or die in office. Some method of chain of command would already be in place should the President be seriously ill for a period of time (say a stroke, cancer, etc).
Abolish department of Homeland Security. These functions were all properly maintained in pre-existing federal bureaucracies (FBI, CIA, NSA, etc). Privatize airport security as well.
Abolish DEA and DARE program and related drug enforcement positions.
Abolish or privatize the postal service.
Abolish department of Commerce, or at least its non-statistical/patent law functions (essentially all commercial subsidies). I guess we can keep the census, NOAA, BEA, NIST and patent office. ITA needs to go.
Abolish the department of Energy. Most of this money is subsidies on coal, oil, and maintenance of DoD nuclear activities (which can be done by the DoD). (about 40 billion total).
Abolish the department of Transportation. Retain or phase out gasoline taxes, but ideally implement more local/state toll taxes on congestion pricing for controlled access roads (ie, highways) instead. Privatizing air traffic control should have been done decades ago. (about 80 billion)
Curtail the department of labour's activities to those related to fair labour practices and the collection of labour statistics (such as employment). Why we need a faith-based and community initiative board funded at the federal level is beyond me already, but why it's seated in the DoL is even stranger.
Abolish HUD. Maintain some basic banking regulations on loans and mortgages and for home construction instead. Local-state governments should abolish rent controls while we're at it. If nothing else, kick out Fannie and Freddie immediately.
Abolish department of Education. Reform payment of schools to create a system of tax credits issued for education spending, payable to any institution of the taxpayers' choice. A similar concept for health insurance and retirement spending may be reasonable, though in all three cases, the government should not control where the money must go (other than that it should be spent on some enterprise related to the tax credit, education spending for the education tax credits, health spending for the health credit), and we should have something like actual health insurance as an option (that is: catastrophic health care coverage with a high deductible, possibly with guaranteed issue, but risk-adjusted premiums, just like any other form of insurance). May end up costing about the same in actual subsidies, but often at the state-local level instead of federal.

Presumably smaller cuts are there to be made to state and treasury, or at least reforms, though neither takes up a substantial part of the budget on its own.

Defence spending
Reduce our nuclear arsenal
Major cuts to defence spending and reform procurement and payment for military. I would suggest about half of the defence budget over a 10 year period be trimmed off. This would still put us at about 3 times the next highest country and the level of the entire EU. Much of current military bloating spending is related to the idea that more ground troops would be needed to fight wars and create occupations like those Iraq or Afghanistan. Such wars are a considerable waste of time and money and do not serve to increase national security. Therefore, the type of thinking necessary to fight such wars is flawed. At best we should retain a high-quality special operations force for such incursions, and move on to other national defence priorities than fighting peasants over rocks. Large portions of spending are also allocated to construction projects in these war-zones. While I do not object to foreign aid as such, I don't see its utility in an active war zone of an occupied country.
Devolve the VA into DoD funding. We don't need an additional special interest group with a seat at the table for veterans over and above active soldiers.

Entitlements.
Block grants for medicaid instead of matching grants.
Voucherized/means test Social security/medicare. Phased in so near-retirees don't freak out.
Alternatively, use a negative income tax and abolish (nearly) all forms of welfare and itemized deductions. This would end things like the home mortgage interest deduction, food stamps, unemployment insurance, social security, medicare, and so on. A downside risk is a few extra lazy people who don't produce anything for the economy. But personally, I'd rather such people not be working. They're not likely to be very productive employees anyway.